Once your Barbarian reaches level 70 (perhaps with a help of a leveling build), you will be in a prime position to pick and work towards your Build. Keep in mind that your Build will not only define your gameplay going forward, but also your optimal armor and weapons.
Below you can find some of the best Barbarian builds for Diablo III.
(LoD refers to the Legacy of Dreams Legendary Gem)
A fast hitting, tanky build that is capable of dealing large AoE damage. It does not rely on any sets, but rather a few legendaries to enhance your Skills. Damage on this build primarily revolves around Hammer of the Ancients.