WoW newbie looking for advice

[Monkey]

It seems that I kill somewhat faster with the additional +spell damage (+20 is there regardless of anything else), but the downtime is kinda getting annoying. Guess I've been spoiled by Spirit Tap.:)

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.