Reinman, Keep in mind that Enchanters can FEAR!! When I used to hunt in the Dreadlands, it was rare, but sometimes we lacked a healer! When we did we would limit ourselves to single pulls, but the Ranger would Snare and the Enchanter would Fear. The group was AMAZED at the power of this combo as no one was really taking any damage. Fear might wear off and someone would end up taking a few shot, by then the critter was usually near dead or I'd just re-Fear it. I wasn't 2-boxing then, but it's still a valid tactic.
Also, make a good hot-key set when 2 boxing. When I'm JUST 2-boxing I have the #1 hot-key (calling it HK from now on...) "Target Keriks" #2 HK "Assist Keriks" #3 HK Rune, #4 Feedback (It's a damageshield, only 11 points and Keriks is now better so I'm going to be deleting it) #5 (Whichever is my best haste) etc.... The last 2 are #9 DD nuke and #0 Mez.
The point of these hotkeys is to make targeting easier. I have my Enchanter mounted and using auto-follow. To target my Ranger I just press the #1 key, the buff by hitting the number of the buff I want to cast. When I want to debuff of kill/mez a critter I hit #2 and the # I want to use. Obviously I put my spell gems in hotkey positions. That's a lot easier than hitting "Alt #" to cast.
The secret to good 2-boxing is doing things as effortlessly as possible, and as quickly as possible. Normally doing it this way you can control the spell-caster much easier and without fumbling around. Make sure all the spells are saved in those positions, consistance is what will make it easier over time and less prone to silly mistakes. Targeting is suddenly a snap with no need to ever touch your mouse. Make HK's for other people if you need to, you can have up to 10 buttons so take advantage of it.
I'd think the best 3 box would be....
PALADIN(Because they can take damage great, heal reasonably between fights, hold aggro really well and Do decent damage (Ranger once it gets it's lvl 57 Healing is okay for this slot too, even though they don't take damage as well)
ENCHANTER(For hastes, slows, basic control when things get bad, has a pet that helps if things DO go wrong, can cast RUNE series which absorbs some damage to make healing less of an issue, and MANA REGEN for less downtime.)
MAGE(Has nice nukes, pets are really SWEET since it's like adding another tank to your 3-box, can cast great Damage Shields.)
Shaman can sub for the Chanter if you really want the heals, but the Pally and Ranger(at lvl 57+) has good enough heals if you ask me. If things go wrong, you'd really want the Chanter as it has so many options to fix those bad pulls. Plus as I said, the Chanter's mana regen is a nice bonus too.
Just my 2cp's, there are a few good combos, but that's what I would like to run myself. I have 3 accounts now too, so I might.
Good luck whatever you decide. I'm curious to hear what you decide and why though so let us know. For my 2-box I happen to be working on a Mage to go with my Chanter so that should be a real nice team.