Barb skills pretty much break down four ways generally: tanky melee, dps melee, thrower, sprinter
Tanky example: Revenge (provocation), warcry (impunity), frenzy (sidearm/maniac), Leap (iron jump), Ignore Pain (iron hide), Wrath (insanity)
DPS will be pretty similar though you may wish to include Battlerage/Earthquake for more damage and drop Leap/IP. Furious Charge (dreadnought) is also a good option for either style given it's mobility and healing potential.
Throwers user Weapon Throw/Ancient Spear with Battle Rage (into the fray) to deal damage from range and keep their fury up. It's a little bit boring to play I hear but definitely can deal good damage. You need a decent crit % to not go dry on fury.
Sprinters are going to use Sprint with the 'run like the wind' rune to generate whirlwinds behind them which when used with battle rage (into the fray) and wrath (thrive on chaos) and some Life on Hit is very sustainable. Can be mixed with Whirlwind or defensive cooldowns very well. Crit necessary to not run out of fury.
Gearing in general is Armor + Str + Vit are your priority stats until Inferno. Attack Speed is always good but it's still unclear how it works with certain abilities (earthquake, run like the wind) so it's mostly a priority if you find yourself auto-attacking (frenzy) a lot.
Once you hit Inferno you will almost definitely want at least a few hundred of each resist; which isn't that hard to find if you wear some All Resist gear and use Warcry with Impunity (+50% resistances). On the AH you can find gear with 80str/80vit/40ar (maybe 70/70/35 or 90/90/45 depending on your means and what happens to be available) for not that much which is easily more than enough to get you started. Alternatively you can kind of split your gear between "high str + all resist" and "high vit + all resist" if you can find it cheap enough and it'll even out. Some Life on Hit will help until you're strong enough to either kill fast or tanky enough to survive with mostly potions and revenge.