Late to the party but...
Level 1: Starter Flaming Greataxe
Level 2: Nicked Greatsword or Guardian's Dagger
Level 4: Carnifex
Level 6: Sword of the Thirty (if you don't have Carnifex or if you're paladin, otherwise keep Carnifex)
Level 7: Twinchopper maybe, but I think Carnifex still wins out
Level 9: Blackrazor
Level 10: Sword of Shadows
Level 13: Riftmaker if you don't have SoS (Blackrazor might still win out unless you're Ravager)
Level 15: Tail of the Scorpion if you don't have SoS
Level 20: Epic Sword of Shadow or Epic Xuum if you don't have ESoS
Level 20: if neither of the above, use borderlands Falchion with filigrees, maybe keep SoS/Tail if low filigree access
Level 21: Great Axe of the Drow Weapon Master if you don't have ESoS or Xuum
Level 22-24: Thunderforged Falchion if no ESoS, Xuum, or weapon with filigrees