A friend of mine is having a birthday in a day or two, and since I'm flat broke I decided to give him the gift of me trying to play wow with him again. We have tried several times before, but the problems I always ran into is that the quests were so mind numbingly boring that I just couldn't keep playing the game for very long. Something that is supposed to be fixed with the new expansion that's coming out.
 
So this is where I need help. The other major problem I had with the game was that I hate the combat. I always play the character in games that can sit back and fire off some powers from time to time and not have to be right on top of his keyboard firing off fifty hotkeys a second and keeping track of several dozen different timers and recharges all at the same time. Which, from my experience, is what the game seems to always boil down to past level 15-20.
 
I was thinking of playing a priest and spec for healing. From what I played of it before it seems to mostly just be cycling through a handful of powers over and over while re-buffing the team from time to time. I figured I would ask the Giant Bomb brain trust and see what you guys suggest for me.
 
My experience with the classes in the past have been with a Hunter to the low 40's, another one to the low 30's, a warrior to the mid 20's, a warlock to the mid 20's and a priest to level 10 or so. I enjoyed hunter, but by the mid 40's I was tired of playing him for some reason. Every time I try to play the game I always end up playing a hunter and it never works out, I'm a pet whore, so I figured I would try to ban myself from using one this time.
   
So ya, any and all help will be appreciated. If not, then I guess I will go with the old close my eyes and pick something at random routine.

" I always play the character in games that can sit back and fire off some powers from time to time and not have to be right on top of his keyboard firing off fifty hotkeys a second and keeping track of several dozen different timers and recharges all at the same time. Which, from my experience, is what the game seems to always boil down to past level 15-20.   I was thinking of playing a priest and spec for healing."

My preferred playstyle is pretty similar to yours.  I'll admit, there's no way I can play a warrior, and my rogue has never made it past 20.  My dk, amazingly has been doing well so far, but she's more flashy than your normal melee class.   As you probably already know all of these classes have that stand back and cast/shoot mode: 
 
Warlock 
Priest 
Pally (holy) 
Mage 
Hunter 
Shaman (resto or elemental)  
Druid (resto or balance)
 
Since you've already tried the hunter, priest, and warlock, you might want to try any of the others. 
 
With a warlock, it seemed to me when I tried the spec that affliction was very much whack-a-mole with your hotkeys, so you might want to avoid that spec.
I like healing, and so my priest, holy pally, and resto shammy have been fun for me.  
Mages of course are glass cannons.  They can do great damage, as long as they don't get hit. 
I understand your issue with hunters.  I was having the same issue with mine for years, actually.  I finally dusted her off recently and have been flying through the levels.  I've found the right pet for me, and I seem to do decent damage, so I've been having fun.  
 
Ultimately though, the choice is yours.

If you like ranged magic damage and the occasional healing, try shaman. You said you don't like looking at timers and stuff, and shadow priest always need to look at the durations of their dots. Ele shaman can just flame shock/ lava burst and spam lightning bolt. Also, leveling with a friend, your dots won't have time to do any dmg at all to the mob so I'd go with a direct damage class

Go Rogue, griefing users is the best thing anyone can do in WoW...and it's hilarious. 
 
Corpse Camping is the greatest thing you can do to someone.

Go with the Shaman and spec elemental. The casting rotation is pretty simple..maybe 2-4 spells. You can heal if needed. A enhancement spec is a little more fun IMO, but its a melee fighter and healing is more limited. 

" Go Rogue, griefing users is the best thing anyone can do in WoW...and it's hilarious.  Corpse Camping is the greatest thing you can do to someone. "