We are fortunate to have 3 very good specs.
Discipline and Holy are both very viable healing specs. Even though they are healing specs, you can still do damage fairly well. It may just take you longer to kill things, and you may have to drink more water.
Holy priests have very powerful healing spells, and a couple of nice group healing abilities. They have Circle of Healing, which is an instant cast group heal, smart enough to heal those that need it most.
Discipline priests try to be a little more preventative. They may not have quite the raw group healing power that a holy priest has, but they are well suited for tank healing, can quickly shield multiple group members, and also can throw a big group heal if needed. They also have penance, which is a flashy big heal that will get you noticed (especially in battlegrounds).
Since discipline and holy are both good, I can't say one is better than the other. Heck, I'm dual spec, so I have both. At some point, even if you wait until 80, you should try each.
If you do choose discipline or holy, first put 3 points in spirit tap while leveling. It will prevent you from having to drink as much.
Shadow is our dps spec, but you can heal ok even as shadow while leveling. Just stay out of shadow form when grouped up as a healer. Shadow is the generally recommended spec for leveling. You can quest faster if you kill things quicker. It's a fun spec. You can send your enemies running in fear, while you suck the life out of them. Later on, you can use dispersion to escape damage and refill your mana, which is amazing.
You can level as any of the specs. Take up skinning and either herbalism or mining, so you will have some cash. Respecing is fairly inexpensive at first, and it's ok to try different things.
Edited, Jul 30th 2009 5:08pm by dadanox