I've leveled two priests... one holy and one shadow. You definitely want shadow for soloing. Like the others said, get your spirit tap first, and go from there. Once you get shadowform at level 40, you'll see a tremendous difference.
That having been said, I leveled both of mine before Blizz made all the leveling changes to the beginnig and OL areas, so it may be much easier now to level as holy.
I enjoy playing both of my priests, but I much prefer my shadow priest if I'm out doing dailies, just for her dmg done. My holy priest is more reserved for healing at this point, although she can still kick some a@! if she's so inclined!