Well, first off, the answer is yes, priests are in demand for raid/party, mainly holy priest for their healing capabilities. Shadow priests are also well considered for their mana and health regeneration, but they're also despised for not being an extreme power in dps, nor in healing, but I would say they're quite in a good position.
As for professions, it depends. If you decide to go for the holy side, and you reach lvl 70 (and can play the character in high level instances), there's an excellent epic equipment you can make yourself if you're tailor, and tailoring it's one of the easiest professions out there, when it comes to leveling.
I made my priest miner and engineer, when I knew nothing about professions. With experience, I decided to change engineering for tailoring, and keep minering because my alter was growing up and it was a good money income and a good support for my alter.
Enchanting could be a pain in the *** to level it up, but it rewards in the end.
Hope it helps.
Heremur.