Shadow or Holy?
It's on an RP server, if that means anything. I've never played anything like this in any game, so I don't know whether I should go more towards damage, or more towards the healing aspect of the priest.
Priests will never match up to a Mage, Warlock or Rogue in damage (they are, however, more versatile in some aspects), even if they are Shadow. Certain aspects of their abilities make them a powerful PvP class (especially on 1v1 duels), but for raw damage, they will never match an allied Mage, Warlock or Rogue who is even half decent.
That said, Priests are also the best Healing class in the game, even when they are not primarily spec'd for it. A competant Shadow Priest who serves the role of a healer (it happens a lot, actually) should be able to out-heal Paladins, Druids, Shamans... what-have-you.
Personally, I find the Discipline tree the most appealing. The simple name can be enough to drive a new player away, but if you actually look at the contents of the tree, you'll realize it has some powerful aspects. Mental Strength allows Priests to have massive mana pools; for example, Sabetha has 7700 mana unbuffed, and that's without Intellect-based gear or a leg/chest enchant. If I put on some gear that I don't like as much, I can get up to 8300 mana unbuffed, which is about 9700 fully buffed.
Mental Agility is also very awesome. 15% Mana regeneration while casting doesn't seem that significant (even when directly analyzed), but when your entire performance depends on the existance of some mana in your pool, every last bit of regeneration counts. When you get three pieces of Transcendence armor (which Sabetha has: Helm, Belt and Bracers), you get another 15% as a set bonus -- that's 30% mana regeneration while casting. I generate about 45 mana/tick (a tick is approximately two seconds) and 120 mana/tick while not casting when fully buffed.
All in all, I actually think Shadow's great for soloing, but it's practically terrible for instancing/grouping if you're going to serve the role of a healer.