Yes, you’ll want a bigger HP pool than for softcore as it doesn’t matter how much damage you could have done if you’re dead.
Yes, not only keep backup copies of gear, when you’re levelling up and get a better piece of gear, rather than salvaging the old piece, put it in your Stash. It’ll come in handy for when (note that’s when, not if) you die.
One of the high priorities for legendary gem is getting a Gem of Ease to rank 25. This is so that when you die, you can put this into a spare level 70 weapon, and your new hero can use that level 70 weapon from level 1, and earn more XP per kill.
Stuns, yes. Fears, no. Almost all Barb kills are made in melee range. Feared mobs are mobs that you’ll have to chase after to kill, and if they’re ranged mobs, they’ll run away and then throw things at you until you chase them down. Goat spearmen, quillboars, succubi - these white trashmobs can and will one-shot you, even on difficulties where you could face-tank a guardian. Learn to dodge projectiles.
Yes, make use of a “cheat death” passive. From Patch 2.7.0 onwards, with changes to followers, each follower now has an ability which also gives you a cheat death. Make sure to take that.
Initially, farm at difficulties where you’re not proc’ing your cheat death at all, or at least not often, regardless of whether that takes you longer or not. If you want to play really defensively, if your cheat death proc’s, run away (in the direction you came from, so you don’t pull new mobs) and teleport back to town, and stay there until the cooldown on it has expired then go back.
Remember, you get one go at this per hero. By all means iron-man / tough-guy it if you like, and fight on despite the cheat death not being available, but you will regret it. You’ll learn when to fight on, and when to retreat, only by hard-won experience paid for in tombstones.
As for a starter build. Well, the “free” set for Barbs in Season 23 is Wrath of the Wastes (the WW/Rend set). If you want to make it a little safer, once your Templar has a “Cannot die” relic, you could equip the Templar and your Barb with the Unity ring (replace the CoE your Barb would usually equip) as this splits incoming damage between your hero and your (unkillable) Templar. This is effectively a 50% damage mitigation. Usually you’d have Mantle of Channelling in the Cube’s armour slot. Consider changing that to the Aquila Cuirass. Mantle gives 25% damage and mitigation, Cuirass gives 50% mitigation, so less damage but more survivability.
Essentially, hardcore is slower to level up, slower to gear and you might want to play more cautiously. It’s not for everybody. Some people love the adrenaline rush of almost dying, almost losing your hero and just getting away with it. Others just get far too frustrated at losing tens or maybe hundreds of hours of progress due to a disconnect and never play it again.
My suggestion is simple. Make a HC Barbarian now, and see whether you like the playstyle or not. That way you won’t have wasted any of Season 23 if you find you don’t.