Ask yourself:
"Do I want to have one of the slowest, most tedious levelings?
Do I want to be able to 1v1 practically anyone as shadow?
Do I want to have 2 very different and interesting healing specs?
Do I like dots and draining a target. Constantly. Slowly. Painfully."
I answered yes on most of those, and here I am, just got to 80! woo..
I do enjoy the healing quite a bit, but found out even though Shadow is effective, it's a pretty boring spec for PvE... (never done PvP stuff)
So here I am, planning to have an alt to dps with, While my priest will stay for when i want to heal, since I do quite enjoy that role.
I heard PvP with a Disc priest is very fun, Shadow too I suppose. I mean, you have damage that heals you and an ally, dots, 2 fears one of which is a disarm, Disperse, a Cooldown that gives back a TON of mana...
It's entirely up to you tbh. Also, think how you feel about the lore/looks of this class. I myself like the Holy light and it's lore a lot, so priest is very satisfying for me.
P.S. Seriously, untill 40-60 you'll drink after every. single. mob. It still hurts, just remembering that...
P.P.S. Psychic Scream is badass.