Sword & Board (d8 one-hander + shield): Increased AC at a small cost to damage, good for tanking. Shield Master feat is decent, but it costs a bonus action and
only after attacking. Fighter is probably better at this than Barbarian.
I like the idea of a Sword & Board Barbarian synergizing the Dex save related parts of
Shield Master with
Resilient (Dex) and advantage on Dex saves from Danger Sense. Go Path of the Ancestral Guardian and you have a sticky and hard to kill tank.
Start with 15's in Str, Con, and Dex and go Variant Human or Mountain Dwarf. At level 20 you would have those two feats, Str 24, Con 24, and Dex 16.
Your damage isn't such that you draw fire in a "we have to kill that guy first" way, but with Ancestral Protectors you disincentivize your target attacking someone else so much (disadvantage
and half damage? and you get this at level 3?!?) they don't really have the option of attacking anyone else.
Of course, the low Wisdom score is your Achilles' heel. Actually, that might be a whole leg worth of vulnerability. But as this is a build you mostly be running in a melee centric group (because prone), hopefully one of those is a Paladin (Aura of Courage at 10). If they're Oath of Devotion, that's even better (anti-charm Aura of Devotion at 7).
Having Shield Master's shove as your only (besides triggering rage) bonus action is less than ideal since there will be fights were the opponents are too big (and a friendly Enlarge from an ally would require their concentration). This is countered somewhat by the fact that you should be getting your reaction pretty much every round. If you didn't, it means the enemies missed all their attacks or they all attacked
you. We consider either case a win.
To recap, you've got a big health pool, good AC, taking half damage from physical attacks and often avoiding all Dex save based damage, forcing one target to focus on you, bonus action shoves made with advantage to give your allies advantage versus a prone target, and mitigating/inflicting damage every round with your reaction.
Sword and Board fighter can do more damage, but can they be a better tank than that?