Lemon curry SMASH!
The more of these threads we do the more my opinion crystallizes. The Barb should be D.) All of the Above.
Background is a no brainer. Throw in the skills. Add Keen senses or some other trait, maybe live off the land type power. Background should be called Barbarian.
Theme is a little tougher, but a rage mechanic similar to the fighter's Surge mechanic would be passable. Rage feats as you work up in level. The theme can be called Rager.
A class is going to require more than hits hard when raging and takes a licking. A Beserker class needs to be delineated from a fighter/ranger with anger management issues. A Beserker should be a mobile shock troop. A charger with little concern for his own welfare. Resistant to mental magic (he's crazy yo) and movement restrictions. I would want to see a rage feature that boosts combat as the PC takes damage. The closer to death the more potent he is. Maybe a building damage bonus per round after bloodied or reduced to one hit die worth of hit points.
The hit die threshold can be expanded with level. The 'Zerk can have some totemic focus that he can expend like the 3e buff spells, Cats Grace, Bulls strength, Bears Heart, Hawks Eye (attack advantage), Stags speed (movement bonus) and Weasels Luck (disadvantage to foe).
Similar to old rage or Surge, number of times per day, the 'zerk can focus his totem to boost for a round.
In the end, the barb can be a class in the PHB if it is complete for publication. If it is not shaping up to meet the polish of the rest of the classes, it should wait for another book. Same for ranger, paladin, monk and assassin.