Deciding a wow character ultimately depends on your play style. Now classes get talent points at level 10 which give them the ability to specialize their wow character in one of 3 ways.
For instance a Warrior can use a big 2 handed axe/mace/sword and dish out the DPS (damage per second) and focus his talent points on the Arms talent tree.
Or He might want to dish out some DPS with 2 weapons at once and go down the Fury tree.
And finally he might want to "Tank" in groups. Which means he gets beaten down by the NPCs(Non-player-characters) in group play, not dishing out much damage but can take a ton of it so he doesn't die before the healers get a chance to heal him.
While pretty much all wow character can have a "DPS" type role, some are simply designed for it no matter which talent spec they go (like a mage) or as a priest where you can choose to go "shadow" and dish out magic DPS OR you can go holy and be a full fledged healer.
So if you like to help groups by healing, you'll want to choose a wow profession such as Paladin, Priest or Shaman.

If you want to Tank a Warrior or Paladin are your best choices.

If you want to DPS a Hunter, Rogue, Mage or Warlock would be your best choices.

If you really just want an easy and fast time to level while doing some good damage with pretty simply gameplay, I would recommend a hunter for most people, probably the easiest wow profession to level in the game since there's very little downtime (drinking/eating) because your pet "Tanks" NPC's for you.