Questions About classes to choose in DUAL boxing.

Hi, I am new in the forum/community, I enjoyed a lot with some Multiboxing Videos (first I watched was Zin 5boxing in Arenas) and now I am thinking about start dualboxing, but I have some limitations.
I am interested in dualboxing for leveling, I am not thinking about run PVE or PVP with dualboxing (at least at this moment).(Of course I am not interested in Account/Character/Gold/Whatever Buying/Selling)
Well, let's get started, I have one computer with one monitor and my 2 wow accounts, I want to level some classes(Warrior>Druid>Priest>Warlock) but I am not sure about that class compatibilities/combinations and, for example, I am not sure about questing/grinding, of course I know I cant level that 4 classes at same time with my 2 accounts, and at this moment I can't buy/pay more accounts, so I will appreciate some Class Combination advises.

My hardware is:
Intel Core2Duo E6850 (3GHz)
2x1024MB DDR2-800 Kingston
Nvidia GeForce 8600GT(512MB)
Logitech G15
17" CRT
(I don't think the rest can make a difference)
With this hardware I am able to run my 2 accounts in 1600x1200 and 1280x1024 @ 30-60fps, of course with one monitor I only see one client/account

While we wait for someone who knows what they're talking about to answer your question, I'll throw my two coppers in.

I'm pretty much in the same boat. Two accounts. I'll likely run two machines tho. I haven't dual-boxed in WoW at all, but I've played 4 accts in DAoC. What I found most fun was sets that had good synergy. I'm looking at starting with Warrior/Priest but I've given thought to Druid/Warlock for the added flexibility. I don't know how "uber" or efficient that would be, but I'm more concerned with what is fun and interesting to play. As for the Warrior/Priest combo - one guide says that is pretty slow, but I'd think its fairly reliable and a good place to start anyway.

Personally I love a mage/priest combo, especially when aoe farming. This was my combination for my first dual-boxing experience, I have since advanced to 5-boxing. If you ever decide to upgrade to more accountsthe mage works well for boosting your own characters. Although mage wasn't on your list of things you wanted to level. I find the healer/dps combo to be very effective and also gives you a bit of versatility for when you decide to group with others

From my experience and using your list I'd say try:

Priest/Warlock or druid /warrior (druid healing spec)

or you could aways do some shammys liek most other people :)

I'm a far cry from an expert as I just started dualboxing not more than a month and a half ago, but I would suggest (as stated prior) the Warrior/Druid and the Priest/Warlock. Reasons I give for this are the Priest/Warlock combo will add much DPS and healing when needed. It will supply you with a tank (void) and if your Priest goes shadow, it ups your Warlocks overall DPS as well. The Lock can place soulstones on the Priest and create Healthstones while your Priest can up your Stam on the Void and both toons.

As for the Warrior/Druid combo, your Druid can supply your Warrior with GotW to up his armor and stats as well as act as either an Offtank or DPS, not to mention his HoTs. Your Warrior, on the other hand, will successfully pull off the aggro from your Druid if such a case arises.

That's my thoughts, hope they help or atleast recap what others have told you or you already knew, haha.

Happy multiboxing!