Rule #1. Avoid melee on your "bot(s)".
Rule #2. A tank makes elites/group quests easier.
Rule #3. Healing makes things go faster, but so does DPS.
Rule #4. Doing instances with 2 people won't work.
Rule #5. You may wish to Raid/PvP with one or both of the toons.
Rule #6. Certain spells/talents complement each other.

Using those rules, select a few combos that work, and pick one.

Just some examples...

Rogue/Priest
Warlock/Priest
Paladin/Mage
Druid/Druid (Feral / Balance)
Shaman/Shaman
Warrior/Paladin