The plus side of playing a priest is that it's easy to get into instance groups. Pretty much, the easier it is for a character to solo, the higher the chance that you're not needed...
Definitely make sure you enjoy healing, and try it in a Raid environment before fully committing yourself to your Priest is my only advice.
I levelled a Priest to help with our guild progression at one point, and got stuck with it for a year until I could feasibly switch from it to something I enjoyed.
As a Shadow Priest, you may not go the raiding route, but there's only so far you can currently go without a Raid guild. Hopefully, the Burning Crusade will give some more options than just strictly grinding raid content in roles that people may not necessarily enjoy.
Threaded Mode