Best Two Person Team to Defeat Normal Untwinked

[Concillian]

Okay there's two class combos you absolutely don't want:

Wiz + Witch Doctor
and
Monk + Demon Hunter

The reason is obvious... they both have the same prime stat and you'll both want the same gear.

weapons are really important for every class, and every class wants the same thing high damage with a +damage modifier and either a prime stat or a socket to add even more damage. So you might want to choose classes that have different weapon preferences too.

Wizards often want 2H weapons, where Monks often want to dual wield 1H weapons... so Wiz + Monk is a good duo.
Two ranged works equally well, as long as it's not Wizard and Witch Doctor, as they want the same gear.
That's pretty much all you need to worry about. The game design has made gear MATTER for every class. It's critically important to the point that it's almost all that does matter.

You probably want to have one person upgrade the jeweler and the other upgrade the smith so you don't have to spend extra gold. If you're running through untwinked, you may actually be crafting things as you level, which will be a significant gold sink.