Everyone has their own take on it, but I can offer what I have gleaned from my own experiences; take it for what you will.
Single biggest tip: Donāt be afraid to die, and donāt let it bother you when you do. You will die, you will lose gear you like, so get used to it. Itās part of the thrill.
Defense is definitely important, but often, offense is the best defense. When I first started hardcore I stacked vitality and regen, which youād see on your paper doll now as toughness and recovery I guess. This works up to a point, but in some cases becomes counterproductive, particularly at high tiers. If you stack defense at the expense of offense, you end up in combat longer, with correspondingly more chances for things to go pear-shaped. So, one piece of advice Iād give is maximize damage output. Naturally, donāt actively skimp on protection and health but those things tend to come pretty easily via gear (more so with paragon levels of course). The faster you kill stuff the less chance it has to kill you. This is the key to moving beyond Master and T1 Iāve found.
Use gems like youāre addicted to bling. Every socket should have the highest possible gem you can cram into it.
Upgrade, upgrade, upgrade. Donāt get attached to gear, only to results. As you level, often a yellow will be better than a legendary. Your earliest set pieces, which you can get in your twenties, wonāt last too long. If youāre in a bounty or a regular rift and you find something better than what you have, get safe and swap it in. Donāt wait. If you need to go back to Mystic it or get a gem, do it.
Clear your path. Donāt leave mobs behind you and rush to the bounty or the whatever. This is especially true when confronted with treasure goblins. Until you are really well geared and/or on such a difficulty level you are nearly godlike, chasing after those buggers is often a death sentenceāfor you.
Donāt underestimate the bad guys. Blue packs have killed more of my guys than bosses.
Get some immunities if you can, via gear or later via Kanaiās Cube and melting legendaries. Immunity to arcane or poison is really sweet.
Learn to move. Tunnel vision can make you stand in the fire/goo/ice for waaaay too long. Make sure your movement speed gets buffed somehow.
Always slot an escape skill of some sort when you can. And always slot the most defensive passive you can until you get comfortable at least. When you get a āget out of death freeā skill like Unstable Anomaly, slot it.
Be prudent. Until you are geared and in the groove as it were, itās better to take more time than to hurry and die. At the same time, donāt dally. āJust one more chestā is a great way to croak after youāve finished a rift.
Start relatively easy. Iād recommend starting on Hard, but Normal is perfectly fine if youāre starting completely from scratch with a seasonal character for instance. If you really want to ease your way in, do the story mode. After you off the Skeleton King, you can then switch to adventure mode. Me, I just jump into rifts at level 1, nearly naked. Itās a hoot.
Always take the Templar. In Adventure mode you get him from the get-go, so grab him. Heās your heal bot. Turn voices off if you have to, but always use the Templar.
In terms of survival, different folks have different views, but Iād put them in this order in terms of toughness (YMMV): Crusader, Barbarian, Witch Doctor, Monk, Wizard, Demon Hunter. Thatās not how Iād rank 'em for fun, but it seems to be true for survivability. The Monk is probably better than the WD until the WD gets going though, or if the WD doesnāt run pets.
Get your crafters to max ASAP if you havenāt already. Donāt be afraid to use the Mystic on everything to get stuff you need.
Give your follower (the Templar, it should be!) rings and weapons that have cool, useful affixes. The Nagelring, which summons exploding imps, is great for Kormac to tote around. Ditto with legendary weapons with useful effects, like blowing up enemies or shooting out lightning. Theyāll work for your follower as well as for you.