Man, a whole bunch of great advice in this thread already, so I’d just like to put in what I personally use all the time and would hate to be without.
Knives. A big as you can handle it chef’s knife and a paring knife. Lots of love for others but if you get a decent chef’s knife it does the job of all the others within 90%. Buy the Victorinox, buy a cheap sharpener, replace it in 20 years when you’ve taken 1/16" off of it. (and get the ten inch, trust me and Aerosmith on that one.)
Food processor. This is a surprisingly important one, it is actually super useful. I wouldn’t even look outside of Cuisinart, and if you can find one that’s 30 years old, all the better. They just work. BUT, you will also have to purchase the lid that doesn’t have all the safety bullshit on it, about $30. It turns it into something you use constantly vs. something you rarely use because use and cleanup is such a pain in the ass.
Good can opener. Don’t sneer at canned goods, if you research it you can find fantastic foods in cans. By good I mean maybe the Oxo vs. the throwaway cheapest, don’t go crazy.
10 or 12 inch cast iron skillet. I’ll argue against some folks and say that they do not require any significant maintenance unless you’re Martha Stewart, Just cook in them over and over and over and let the fat sit from breakfast to dinner, there’s nothing that’s going to hurt you between 8am and 8pm. When they get too rough from accumulated burnt fat, grab a pack of steel wool and go to town. And don’t be shy to clean them with scrubbing pads and degreasing cleaners like Dawn, it’s an old wive’s tale that it ruins the seasoning. That seasoning is a layer of burnt carbon, if Dawn could cut through that without an angle grinder, then Dawn would be an industrial product. Clean it, wash it, heat it, oil it, keep going.
A comfy several spatulas. Again, the cast iron won’t give up the seasoning if you get in there and scrape around with a steel spatula, go nuts. I like to have at least two going because one is always dirty in the sink.
New one: Bench scraper. Should be two bucks for a plastic one, and that’s fine. It’s wildly useful for what its name says, pick up your board and scrape your bench into your hand or a dirty pan or whatever. Quick cleaning means more cooking.
Another new one: Swedish dish rags. I just got onto these and they are great. Think a paper towel that is thicker, much more durable, washable, and dries like nobody’s business. I don’t like waste and these are the solution to paper towels in many scenarios.
Non-stick pan. You do need one. In fact, I would argue it’s not a bad thing to have two, but if you watch for sales you can find them cheap. They don’t do high temps safely, and they need to be babied a bit re: the steel spatula (get another plastic one for this specifically) but if you keep them perfect, they work as advertised. I even bought some All-Clads, which is probably the de facto “good stuff but not stupid good stuff” brand for 20 bucks apiece for an 8" and 12". Macy’s has good sales on these.
Saucepot, small and large. Honestly, I do love All Clad again for this but I bet there’s a KitchenAid version that does just fine. Stainless is always going to take more work but sometimes you just need it.
Cutting board: Whoo boy, I gots some opinions. End of the day, the best possible cutting board is a super thick endgrain maple board. If you can see the grain in it, then it isn’t endgrain, it’s face grain, and that means that when you cut it, you cut the fibers and they never come back together. End grain is friendly to your knives and somewhat self-heals when you oil it. A good cutting board never leaves your counter, it’s a counter all its own. They can get silly expensive, but if you invest in a big bastard, like 12x20x2", then it will be the first and last one you ever own. Go to the laxative section of your pharmacy and get a $2 bottle of mineral oil and soak that sucker until it can’t take any more. Once the color starts to fade, hit it again. If you had a table saw and clamps and whatnot then you could look around for a butcher-block tabletop offcut and make your own, but I think that’s probably not in your wheelhouse right now. Butcher-block counters are usually face grain, which is fine, but not what you want for a forever board.
Big stainless bowls. Buy some. Small medium large, and by large it should be a foot or more across.
Measuring cup. No need to spend big dollars here but get a good 2 cup pyrex cup with imperial and metric gradations.
Basic wooden spoons. Cheap as heck and you can’t have too many.
Colander. You need one, don’t go crazy. Anything enameled is just fine.
Cheese grater. Same as above.
Vegetable peeler. Again, Oxo does a fine version. When you start doing 2 star ratatouille then upgrade.