Honestly, I've never liked playing a priest until at least the mid teens when you can finally have Mind Blast, Psychic Scream and Spirit Tap. For whatever reason Blizzard was just really stingy when it came to handing out low level versions of some of the best priest soloing tools. It always hit me as kind of silly, particularly compared to warlocks,* who can end up with a pet, 2 dots, Curse of Weakness and a nuke by level 4, all of which have rather obvious solo applications. By level 10 Locks get two pets to choose from along with good ol' Fear and Lifetap to play around with as well as a third dot. Meanwhile Priests are adding Fade, Resurrection and (thank God) their first rank of Mind Blast. Nothing wrong with those spells, mind you, it's just that only the last one is really useful at level 10, which is something that hits me as a rather needlessly discouraging.
*That is meant in no way as a dig at warlocks. Low level locks are fun and powerful; if anything they should be seen as a shining example.