With low gear I'd start with a 1h and a shield, take a nice AoE DPS build (WW, HotA, Avalanche etc) with some defensive passives (Tough as nails, Nerves of steel etc) for a fast toughness boost to get yourself into torment 1 ASAP.
For my barb I spend my paragon points:
Core: All strength
Offense: Crit chance until ~50% overall, then crit dmg
Defense: Life if you have resist all gems, else resist all. (you'll be standing in a lot of AoE on a barb)
Utility: Life on hit
Two big gear shortcuts are to make yourself a decent sovereign amulet, rerolling the stats for decent crit values (up to 10% crit chance, 100% crit dmg) and pick up a rare quality weapon you can reroll into a gem socket for the extra crit damage emeralds give. Rerolling rare items is dirt cheap compared so you can end up with +230% crit dmg for 2 minutes work before you start farming.
Also, I've not tested this but having a magic find gem in your helmet may help you get up to speed with gear a bit faster.
It's very early in the xpac now, so don't expect miracles. Find a nice profile, turn up your toughness until you can survive on torment 1 and wait for the damage gear to drop.