Wow is one of those games that gives players LOTS of choices. Although there are nine classes in the game, talent tree decisions can make that number seem much higher (I wouldn't quite say 27 because some classes play similarly regardless of spec). How can someone find the "right" class to play with so many choices? You just have to experiment and play what feels right.
Another thing that makes the whole thing murky is the concept of the endgame. Blizz has set the first 79 levels (soon to be 84) up as this time of continuous improvement and advancement, mostly done solo. You are more powerful than most of the mobs you'll fight one on one, and you can usually take down multiples at once, sometimes with a short time to rest and refresh afterwards. Then you get to the level cap and everything changes.
I have found a couple things in my leveling of multiple characters in the game. In solo content melee characters generally have an easier time of it. Three to four mobs on a paladin, death knight or enhancement shammy are nothing. Three to four mobs get up to a priest and I'm freaking out, dotting them up, dispersing, and praying they die before I do. However, this has no bearing at how things will play at 80 apart from dailies.
I have found "the game" at 80 to be an application of fast AoE on trash, and sustained single target damage on "bosses". I prefer accomplishing this at range for easier targeting and safety. For me, caster DPS is the way to go with additional points given for utility. This is what feels right for me, your feel for the game may be completely different. Rogues, who lack utility and can only melee DPS are useless to me. Hunters who have solid ranged DPS but no other utility are equally so. Warlocks and mages have some measure of additional utility, but fall short of the druid, priest and shammy's abilities to heal. That is a HUGE benefit to me, in addition to any other buffs they provide groups.
The last thing to consider is how the class makes you feel. I have not leveled up a priest all the way to have an accurate comparison. However, in playing my shammy elemental, I just get a little giddy inside. 7.5k crits from lava burst, sometimes I literally say "BOOM!!! You're dead!" Shammy is just enjoyable. Priest might be just as enjoyable, I don't have a point of comparison yet.
What feels right to you? Try to step outside the box and give other classes a chance, you might find one you really like.
Mid Afternoon Quickie
4 years ago