It depends on what type of character you want to play.
DPS - Warriors, Rogues, Mages, Warlocks, Hunters
Healing - Paladins, Shaman, Priests, Druids
DPS & Healing - Shaman, Priest
Melee - Warriors, Rogues, Druids, Shaman
Ranged - Mages, Warlocks, Hunters
Figure out if you'd rather be up close and personal, or back on the back lines.
If you just want to get the hang of the game, I'd reccomend a hunter or a warrior, and tell you to play them to level 20, so you can fugure out the game. After that, if you don't want to play anymore, that's fine, you'll have gotten the basic idea of the game/talents/etc.
I'd figure out what you like to do and what you're good at. If you a multitasker, try a healing class, like a priest, or a druid.
If you like to lead a party, play warrior.
If you want to PvP, try a rogue or a mage (Shadow Priests and Warlocks are fun, too.)
If you enjoy soloing, Paladins and Hunters are great.
If you want to point and shoot, warlocks, mages, hunters and rogues all are good.
Most importanatly, have fun and good luck!