If I was levelling a priest again, I would do:
10-14 Wand Spec (This assumes you are not on a brand new server. On a completely fresh server where you are levelling quickly, you can skip wand spec since you will be limited to world drop wands. In any other case buy all the enchanting wands and be utterly overpowered into your 30s.)
Now start building your shadow tree:
Talent Calculator - World of Warcraft
That is roughly what it should look like at level 37. ISWP before Focus, Reach before Weaving. Now grab another two points in whatever. Silence usefulness varies by server and grinding location, but is probably a good choice. VE is pointless before shadowform. When you hit 40: Respec.
Up to this point your kill method has been dot, nuke if mana allows, wand to death, renew yourself if needed, repeat. Nuke frequency has increased during the last few levels as the relative power of your wand has decreased. You have been stacking spirit along with what little spelldamage has been found. Now you turn into a spellcaster instead of a magical hunter. Your gear should change accordingly with much higher emphasis on +damage through tailoring items and shadow wrath items, but spirit is still your second best stat.
Your new spec:
Talent Calculator - World of Warcraft
Imp VE can be replaced by Silence according to need. You're now grinding in shadowform with VE, and finishing mobs off with wand once they hit you. MB -> SWP -> VE -> Flay (-> Flay) -> Wand. If needed due to a resist or engaging mob from too close, rank 1 fear is superior to PWS for pushback avoidance, assuming you don't pull adds. Unless you are utterly twinked to the gills with +damage, you probably want to grab Wand Spec for your next 5 levels, as it's still a considerable part of your damage and the shadow talents here aren't that awesome. Then fill out improved VE, shadow weaving, and Silence. Now you're 50, and respeccing again (unless you skipped Wand Spec).
Talent Calculator - World of Warcraft
New order VT -> SWP -> VE -> MB -> Flay (-> Flay) -> Wand. At this point start building up the disc tree. Wand Spec > UW unless twinked or doing PvP. Martyrdom first in tier 2, then IPWS. Inner Focus first then Meditation. Put the last 5 points into Shadow Power.
Welcome to 70.