Well, usually it's nice if one of the classes has healing ability (Paladin, Priest, Shaman, Druid) and one of the classes is a sturdy tank/dps sort of class/spec (Ret/Prot Paladin, Feral(tank or dps) or Balance Druid, DK, any warrior, hunter (pet tank, trap utility).
Sort of a healer + tank thing, but for soloing so the tank doesn't actually have to BE a tank, just someone who can deal with being pounded on while the other person heals/supports/nukes.
Or you can do the same thing except with dps + tank, and again, not an actual tank really. One person holds on, other person AoEs like crazy. Good dps classes for that are things like Warlock or Mage.
If one of you actually has a preference to what you want to play, then try to pick another class that does something different. If they pick a squishy class, pick a sturdy one, if they pick a sturdy class, pick a squishier class that can heal or AoE well.
Also try to pick classes that won't compete for gear, i.e. should use different armor types. This will be less annoying if you do dungeons or find world drops or whatnot.