Every race is perfectly playable for priests.
However, alliance side, I would be tempted to go Draenei because I like their starting area so much better than the others. The quest chains are more fleshed out and enjoyable.
If you plan on doing heavy PVP, be aware that the Dwarf racial abilities and spells are extremely good for PVP. Stoneform helps immensely against rogues, hunters and druids, Chastise is golden vs. other casters, and Desperate Prayer is superb. Also, if you play a female Dwarf, you will stand out in any crowd.
Night Elf Shadowmeld is great tactically in PVP, and Starshards has become quite useful in recent patches. However, you will be a night elf.
Humans' spirit bonus makes them quite strong in late-game PVE, and their reputation racial makes grinds somewhat less excruciating. They also get Desperate Prayer, and if you want to Mana Burn yourself, you get Feedback.
Finally, returning to Draenei, their hit aura, Gift of the Naaru, Chastise and Symbol of Hope are all solid advantages. Have fun with whatever you pick!