WoW newbie looking for advice

[Lissa]

I'm guessing that you have Blackout instead of Spirit Tap. I'd encourage you to put Spirit Tap back in your build. It has much better returns for a leveling build and won't adversely affect your killing speed. Here's are my 36 Priest's current talents: Link-O!

This is probably something that you've already figured out, but a typical grind cycle for lightweight mobs might be:
Mind Blast>Mind Flay>Shadow Word:Pain>Wand

For heavier mobs or when I'm feeling saucy:
Mind Blast>Mind Flay>Shadow Word:Pain>Psychic Scream>Mind Flay>Wand

Keep Inner Fire up at all times and either toss a renew on yourself between mobs, or use a bandage every third pull or so. I think you'll find your downtime substantially reduced.

SW:P first, always, always, always, always. The only time that this is over ruled by is when you get Vampiric Touch at level 50. DoTs always go up first for a Shadow Priest.

Here's how you pull as a Shadow Priest as a sub 50 shadow Priest:
Cast SW:P while backing up, cast Vampiric Embrace while backing up, cast Power Word: Shield while still backing, when global cooldown finishes, cast Mindblast, cast Mind Flay, then cast Mindblast and Mind Flay and use wand while reapplying Shadow Word: Pain and Power Word: Shield as needed.