Personal take that is about as subjective as I’ll let myself get in this post:
If gas is an option, consider it. They’re a little more maintenance-y than electric cooktops, but generally heat faster, get hotter overall at most low-to-medium price points, cool instantaneously, and let you do a handful of things you straight up can’t do on electric (e.g., blacken peppers or puff Indian breads like rotis). Way better for shaped pans like woks, too.
An induction cooktop solves some of those issues (speed of heating and general BTUs-per-price-range), but still can’t do the neat stuff that actual fire can.
Anyway, being stuck in an apartment with only electric hookups for the stove is one of my great regrets for the last decade.
Okay, on to actual advice.
There’s been lots of good stuff mentioned so far.
Knives + Cutting board
Buying a bit set of knives is usually a nonstarter. You’ll get a bunch of cheap knives in shapes/varieties you’re not likely to use as a starter. Spend money on 2-3 medium-quality knives, a honing steel, and a decent handheld sharpener, and you’ll enjoy 80-90% of the function of high-end crazy expensive knives hand-sharpened daily on a whetstone, at 20% the cost and 10% the effort.
The Victorinox recommendation is great. Their 8" chef’s knife is an absurdly good value for the money. If you want to step up, yeah, JAH and/or Wusthoff are great. Stainless steel is much better for a starter than trying to get fancy with carbon or cheaping out with ceramic. Folded/forged blades are maybe nicer/better than stamped steel, but I’m not sure the difference is worth the cost if you’re trying to outfit a full kitchen for $1k, tbh.
Some things to think about: western-style knives traditionally had a slightly, uh, “wider” blade wedge/shape. They thus were a little heavier, on average, so maybe better for getting through some tough-to-cut-things, but also not quite as smooth for precision work. Japanese-style blades had a narrower base angle and generally lighter blades. These days, a lot of “Western”-shaped knives (including the Victorinox chef’s knife) use the traditional Japanese angle.
This mostly matters for what sharpener to buy/which sharpener hole to stick your knife in.
I think a good-sized chef’s knife and/or santoku is enough for, like, most stuff you’ll do day-to-day. If you like, a smaller 3-4" paring knife is handy, but tbh, even owning a nice one, I almost never breaking it out. A boning knife is very handy if you’re specifically going to, well, de-bone shit. A serrated bread knife is a huge boon if you’ll be working with loaves frequently. I wouldn’t get more than those four to start, and frankly, you can probably just go with a chef’s knife and be fine initially.
When using your knives, give them a few passes on the honing steel before each major use. Sharpen every few weeks/months, depending on frequency. Youtube has great advice on both.
A good cutting board is a huge help. Get a big one. Big as you can easily fit in your sink, or slightly larger and accept the annoyance. Plastic is easier to care for and cheaper, but slightly harder to disinfect if you’re not gonna have a dishwasher (clean it well! get into the grooves left by knives). Wood probably helps your knife stay sharper longer if it’s a good medium-hardness material like teak, and has some natural antimicrobial qualities that might help slightly (bacteria get trapped in an anaerobic environment when the wood pores close up as it dries out), but you’ll need to buy some food-grade mineral oil to oil it every few weeks/couple of months. And def never stick it in a dishwasher if you get one later.
Seriously, get a big one, though. If you want, grab a small one, too, for quick tasks when you don’t wanna deal with washing the big one. I use a small plastic one for cutting meats, and my big wooden one for everything else (including working with pastry dough and the like).
Cookware
Some kind of high-heat, oven-placeable skillet is a good idea. Stainless steel is super multi-purpose, and a good multi-clad one will conduct heat very well. They’re medium-weight, tons of options at every price point, overall a great idea. Cast iron is heavier, and retains more heat. Great for baking in. But very heavy. And maintaining the seasoning is gonna require some reading on your part. Carbon steel is the new kid on the block, very light, crazy heat distribution. They’re somehow even more obnoxious to season/maintain than cast iron, IMO, but they do have their uses. I’d go stainless steel personally.
Some kind of large, medium-quality nonstick skillet is also good. 10" minimum. 12" is pretty great, IMO. 14" gets a little crazy, hah. Tramontina is a solid pick here. Understand that no nonstick is immortal. You can avoid using metal in there, avoid heating it too high or without food in it, but eventually, it’s probably going to start to break down and flake. Replace it, and be glad you didn’t drop $200 on it. I’d avoid the new-style ceramic nonsticks; they develop hairline fractures from pretty routine use and rapidly lose their nonstick properties with routine use.
A small and large saucepan with a good-fitting lid, plus a larger dutch oven or stockpot style pot. 1/1.5qt, 2/2.5qt, and 6qt, or thereabouts, are good sizes to consider. You can go either/or with stainless steel vs. nonstick here. You can heat the stainless steel ones higher, and you’ll get a better sear on stuff in stainless steel, but they can be annoying to keep spotless; Barkeeper’s Friend is your, well, friend. If you go this route, again, a tri-clad style choice is good. Even if it’s just the “cap” style cladding with the extra layers only on the bottom. Fully clad cookware is crazy expensive. Nonstick won’t last as long, again, but is way easier to clean, and great for stuff like English-style scrambled eggs, or porridge-y things like oatmeal, that tend to stick in steel. One note: if you take @Timex’s suggestion and grab a stick blender, some of them might scratch up a big nonstick pot, and a lot of potato mashers are also metal and could scratch it up. The fancy emamalized cast iron dutch ovens are very nice and retain heat super great, but keep in mind they are CRAZY heavy, so they can suck to wash, and the enamel WILL crack if you don’t treat it right. No links here, cuz the ones I’m using are super hodge-podge.
Funkier skillets/pots, like woks, tawas, crepe pans, sauciers, etc., all have their uses, but, well, you’ll know when you need them.
A set of solid aluminum, thick, uncoated aluminum baking sheets is a great investment. Nordicware brand is pretty awesome, but there are others. Don’t cheap out and get thin ones: they warp and pop much more easily. It’s tough to keep the not-nonstick ones looking beautiful, but, that doesn’t bother me much, and they’re more durable, as usual. One or two each of quarter- and half-sheet pans is a good call. You can easily find mesh racks that fit into the half-sheet ones especially, for stuff like bacon that you want to bake elevated off the pan so the fat can drip off, and they double as cooling racks for stuff like cookies, and are only like $10.
If you’ll be more seriously baking, a 9x13" casserole dish, a 1lb or 1.25lb loaf pan, an 8x8 square pan, and a round cake and/or pie pan are all good calls. Metal vs. glass is, well, up in the air. Metal will heat better and brown the bottom of stuff better, but you’ll probably want to go nonstick (USA Pan is a great brand). Glass will probably cook more evenly overall, but less browning on the bottom, and you do need to take care moving even tempered glass from cold to hot or vice versa. Cleaning shattered glass sucks. New pyrex less good than old yadda yadda borosillicate whatever.
Non-appliance gadgets
Get a good set of measuring cups. Metal ones are nice. Ones that interlock are great. Make sure it’s easy to “level off” (e.g., the handle shouldn’t be higher or lower than the top of the measuring cup, so you can swipe a knife across the top to level off the measure). Use these for “compressible” solids like flour, sugar, rice grains, etc. If it’s very compressible like flour, spoon it into the measuring cup from the container, then level it off with a butterknife. Recipes assume you’re doing this.
Get a good liquid measuring cup or two. Glass won’t pick up smells, but break more easily. Good for microwaving liquids in though. Get one with easy-to-read measurements, a pouring spout, and a handle that fits your hand. Etched+printed measurements are better than just printed; those tend to wash off more quickly, which sucks. At least a 2cup one to start, and maybe a 4cup one if you cook for a crowd frequently. The fancy tall-thin ones with a plunger for viscous liquids like peanut butter or honey are nice, but definitely not needed to start with.
Get good measuring spoons. The things that apply for the cups apply here, too: clear measurements, durable material, stackable or otherwise easily stored. I tend to keep two sets. When I’m cooking, I can use one for “dry stuff” and one for “wet stuff” and not worry about having the wet ones get dry stuff stuck to them, and since they’re cheap, it’s easy enough.
Get a good set of mixing bowls. Maybe two. Metal or glass are great for being able to take a little heat, like when you wanna set them over simmering water to melt chocolate or work with certain egg preparations. Ones that have good sealing lids can be a handy way to store stuff in the fridge. I’d avoid ones with spouts, just because they make it harder to get a good sealing lid on there. Plastic are cheaper, but MANY brands are super thin/brittle, so, be wary of that.
Get a good set of food storage containers. I like the OXO glass ones w/ the teal rubber gaskets. They don’t pick up smells/stain as easily as plastic, are great for microwaving, and stack well. But, obviously, well, glass can break. Rubbermaid Brilliance are an awesome brand of plastic, if you’d prefer. I love using their big ones to store stuff like flour that wants to be airtight. TBH, though, just getting a big box of mixed “deli containers” (1cup, 1pint, and 1quart) with lids is very cheap and effective. If one warps or stains, toss it (please recycle).
Get a couple of good stirring spatulas/cooking spoons. I like a modest-sized, fairly firm rubber spatula. they’re great for getting the last bits of food out of a pan with their slight “suction” that the rubber gets, and a firm one won’t flip-flop when moving through thick mixtures. I also like a slightly wedge-shaped wooden spoon/spatula. The slightly thin wedge-edge is good for breaking up meats or veggies in a pan, and they are a little sturdier than even firm rubber spatulas, and if it’s got an angled wedge-shaped head, it’s great for getting into the corners of the pan. If you get any metal ones, use them for serving only; don’t stick em in your nonstick cookware.
Get at least one good flipping spatula. A thin, flexible head is great for getting under sensitive things like fish, but a study build is very nice for handling thick stuff like burgers or grilled cheese. I like a thin metal fish spatula and a thicker plastic one in this case. At least one should be plastic/rubber/wood for the nonstick cookware.
A good medium-sized metal whisk will come in handy constantly. You can get a couple of different sizes, but, meh.
A decent box grater with a sturdy handle and at least a couple of different hole sizes is good, but don’t feel the need to go get like an 8-sided mega-grater. A good microplane/zester is nice for citrus and hard cheeses like parmesan, but it’s a fairly specific tool.
A vegetable peeler is essential if you’re cooking with, say, potatoes a lot. On the other hand, you might never ever need one. Doubles as a handy cocktail tool for getting citrus zest peels off. I strongly prefer the Y-style, other people love a vertical swivel peeler. They’re cheap. The blade will dull. C’est le vie.
A metal bench scraper is handy, but not essential. Good for gathering up chopped veggies and dumping them elsewhere, or cutting up pieces of dough when baking.
A set of spring-loaded tongs is nice for anything from flipping food to fishing stuff out of a pot. The ones with detachable plastic grippers are nice for nonstick, but they tend to come off into your pot when you least expect it; the all metal-ones are more reliable. I’d get at least 8", but probably not more than 10".
At least one good mesh-style metal strainer with very small holes, decent-sized, and ideally maybe a slightly larger rubber/plastic one, are also both super handy. Good handles are a must here: don’t want to lose grip when you dump 4 gallons of boiling water and pasta into it and the steam hits your hand.
Get at least one good oven mitt. I like the thick, towel-looking woven ones, but the fancy heat-proof metal-woven ones are cool as fuck, too. A rubber-and-cloth heatproof towel or mat to put hot cookware onto out of the oven or stove is nice, but nonessential.
Get a decent set of kitchen towels. I like the restaurant-style basic white, thin ones, usually with a colored stripe. Zepoli makes some I like. They don’t soak up a TON of liquid, but they’re durable, flexible, and thin enough to use to strain stuff, and are great for covering dough while it rises, and they’re cheap enough you don’t mind getting them gross. Avoid super fluffy ones; the fuzz gets everywhere.
Get a solid can opener. Nothing worse than being 50% of the way to dinner and your fucking cheapo can opener breaks and you can’t access your last four ingredients. A bottle opener is a somewhat less vital option.
A couple of different sizes of springloaded ice cream scoopers are nice if you eat ice cream and/or bake cookies a lot, but very much ephemeral. I’m just a fatass that loves dessert, hah. The different sizes are great for portioning thick doughs, like cookies or falafels.
A citrus juicer is handy for really getting all the juice out but avoid most seeds, but non-essential. So, too, potato mashers. TBH, I kinda prefer the ones with small holes rather than the wire ripple kind, but, they’re a lot less sturdy in my experience.
Very situational, but a good stone mortar and pestle with a wide mouth and lots of room is great for very specific things. Crushes nuts like whoa but obviously intended for stuff like making pesto or guacamole the traditional way. I just happened to walk into my kitchen for lunch and saw mine, hah.
Appliances
A good microwave is a very handy thing indeed. Some food just sucks to warm up otherwise. Rice comes to mind. I hated rewarming rice w/o a microwave, ugh. Something big enough to fit your larger glass measuring cups/bowls/plates, obvs.
A toaster oven, esp. one with convection functions, is, IMO more flexible than an air fryer, but maybe less good at specifically air-frying if that’s exactly what you want, unless you get a very pricy one. But they’re great for reheating things you want to be crispy, or for baking small quantities of stuff when you don’t wanna heat up the whole oven. I love pizza rewarmed in a toaster oven vs. microwave, for instance.
A good stand mixer is better than a hand mixer, but they’re pricy, I know. They’re great for baking, but not a LOT of other recipes will really call for one, or can’t be handled by more labor doing it by hand. But Kitchenaid is the standard for a reason. The Artisan line are a good starting point.
A slowcooker is nice if you’re just starting out, but genuinely, I only use mine for keeping food warm at parties now. If you want super low effort, cook-while-you’re-at-work stuff, though, they’re nice. Don’t break the bank on this. Get one with Warm/Low/High and MAYBE a timer if you’re feeling fancy.
A fancy electric pressure cooker like the Instapot does several things pretty okay. Most of them slow cook well, pressure cook well, and maybe even rice-cook well. Specialized tools do each of those things better, but an all-in-one is handy, and LOTS of popular recipes right now assume you have one. Not a bad investment, again, esp. for a beginning cook. They can save a ton of time. Beans in 15 minutes instead of 90 is nice!
A good blender is also nice. Don’t go crazy, but you get what you pay for. If you love smoothies and get a $20 blender, you’re gonna have big chunks left and a weird mouthfeel. They’re nice for blending up sauces, milkshakes, cocktails, smoothies. If you do sauces, beware of putting hot stuff in. Google it, and be safe :)
An immersion blender is fairly specific but VERY handy. Blending up curries, chowders, cream soups, etc., in the pot you’re cooking in is super handy, and if yours comes with the right sized little blending cup, you can even do homemade mayo with one in like 20 seconds. Don’t need to break the bank, but it is a very handy, but not fully essential, tool.
A food processor does different things than a blender. Great for breaking down meat as a poor man’s grinder. Whip up falafel dough. Quickly put together pie dough. Make hummus or guasacaca. Not an absolute essential, but if you’re gonna get one, go ahead and get a bigger one. 9-12 cup probably. 14 is a lot. PS, these usually aren’t fun to clean. Lots of little pieces. Sigh.
A good toaster is faster/easier than a toaster oven, but if you have space and only want one, the toaster oven is more versatile. If you make a lot of bagels or toast big artisan breadloaves a lot, make sure you get one with wide/long slots. Metal ones heat up on the outside, but look purdy.
A kitchen scale with a tare function, easy-to-read display, and metric/imperial measurements is super handy if you bake a lot, but comes up in a few other situations, too.
A good probe thermometer is very handy for checking the doneness of everything from meat to bread to baked potatoes. Get a quick-read one, if you can. A deepfry/candy thermometer is nice for those two specific tasks only, but if you do either, it’s super good, and they’re very cheap.
Weird one, but I love my cheap $8 milk frother. It, well, does that. Sometimes I use it to whip up a couple of tablespoons of cream with a bit of sugar to make my gf Asian style milk cap tea. Super not essential, just a weird gadget I kinda love.