I just finished getting my new Draenei Priest to level 10, and I've had a fun time doing it.
First off, as a priest you start with two spells: Lesser Heal & Smite. And you can hit up the trainer and learn Power Word: Fortitude, right away. I was able to handle all the mobs in the starting area with Smite. The quests in the Draenei starting are well-connected and flow well, plus it was easy to kill mobs for extra xp.
Level 4 - I picked up Shadow Word: Pain, and this DoT made handling mobs that much faster.
Level 6 - Power Word: Shield is a great spell. I would throw Shadow Word: Pain at a target, pop Power Word: Shield, then wail on them with Smite. Just from my experience with this spell, I've decided to level this toon as Discipline. I also moved to Azure Watch and started working on the quests there. I also caught the end of Noblegarden, and was able to do the quests for that, and found the Spring Rabbit's Foot.
The furbolg questline in Azure Watch is one of more fun and interesting one's in the game. I like how each of the totems gives a different ability for a short period to get you to the next totem. Be careful once you reach the final totems, the furbolg here will aggro on you, they patrol and call their friends.
Level 8 - Picked up Fade and Renew from the trainer. Haven't had any use for Fade yet, but renew is useful in soloing questing.
Level 10 - Learned Mind Blast and new rank of Lesser Heal.
If you haven't done the Draenei starting area yet, you should try it out.