1. Be a Nord. (I could be an orc, but orcs are just Nord wannabe's.)
2. Use two-handed weapons.
3. Bows are acceptable.
4. Sneak. Barbarians sneak. They also open locks, but without a decent lock bashing system, picking them becomes acceptable.
5. Armor should contain FUR. Exception: Ancient Nord armor is always acceptable because it's ancient and it's Nord.
6. Avoid all magic made by foul sorcerers. You can't trust 'em. Exception: Anything ancient Nord is acceptable because it's ancient and it's Nord.
7. Barbarians wear the trophies ripped off the backs of their enemies. They don't run around making armor. They tough it out. (Although if an NPC is willing to improve it, that's OK. That's what servants are for.)
The only point is playing a barbarian is to hunt down and kill all 1) Dragons, 2) Dragon Priests, 3) Wizards, 4) Sorcerers, 5) Witches, 6) Imperials, 7) Enemies, 8) Invaders, and 9) Everyone Else.