Throughout the first couple of expansions nothing beats enchanter/cleric. Charmed mobs will outtank and outdps anything else in the game, and with a substantial health pool the only class that can effectively heal them is the one with complete heal.
For a third, you can add a porter like druid/wizard, more dps (caster of some sort, mage has both malo and coth), a puller if you don't feel confident pulling with the enchanter, or a bard if you just want a selo/melody bot. It does take a bit of skill to charm though, and you have to be ready for charm breaks at any point in time.
While I think the above is by far your best bet up until and maybe including PoP, the other option would be to go something like sk/shm/mnk. Slow is great, monk dps is insane, sk is a solid agro tank. This combo is probably a bit easier to play, and a bit more forgiving overall.
Truthfully, I think it just depends on what you find more fun, charming is incredibly stressful and you cannot really afk to go to the toilet or eat without killing off the pet or camping out etc. Worst case scenario you can always power level some new classes later on, or add more accounts into the rotation -- in this case strong power leveling classes might get some additional value in your original 3, like say a druid.
