Those are the 3 big ones to look for ye, things like +crit, +movement speed also comes in usefull. A 2hander barb in NM takes alot of dmg, alot, so i spec my barb to grant various kinds of +healing when i crit, shout, +armor when i leap etc... As u said, the weapon is by far the most important gearpiece since all abilities dmg depends on it.
I've never tried, or even considered, using a shield as a barb. Dualwielding can do almost as much dmg as a 2hander. Not sure, but i think the lowered killspeed of 1h+shield isnt worth the extra survivability.
I havent bought anything on the AH yet, the weapon prices are insane to say the least, i do well with what drops and hand-me-downs from mates playing barbs in hell.