Well I am biased because I have a priest but holy priest healing right now is no cake walk. I would have to say Pally healing is the easiest...one button ftw! But priest are easier on Disc because they have little to no mana problems. Holy priest is definitely a challenge especially after the spirit nurf but if you get a good spell rotation down you are bound to be just fine.
Shamans are interesting, I get annoyed easily with mine just because of the stupid totem bag space issue. But as for heals, you have to be a pretty good shaman to get anywhere near the top of the healing list.
I personally love druid heals because they are so unique. I love the stacking and such and as a druid you will never have a mana issue and its pretty easy.
Leveling a priest I would suggest you check out the Holy Warrior Priest build as it is good for healing experience and easy to level with. You still pack a nice hit and you don't run out of mana. Then again I wouldn't hit that spec until you reach 40 or 50.
I just wrote all of this about healing classes and spec and didn't even realize you might be talking about DPS'ing with one...sorry! haha I have opinions there as well!