Hearthpwn

This deck KILLS priests!  Against priest/mage/warlock/Druid always hard mulligan for Divine favor (keep small time recruits and Finja though).  The goal is to keep spamming your hand, do as much damage as you can before they clear,  draw more, repeat.  Soon, the they will run out of board clear, you'll be close the bottom of your deck, and you'll easily win with 1-2 Anyfins.  My win rate is really high against priests and warlocks (a little lower against mage because iceblock and Druid because, well, druid), and really only lose against priest/warlock these if I fail to get card draw.

Against faster decks (shaman, hunter, warrior, Rogue, Pally), hard mulligan for Muster for Battle (but always keep Finja).  Try your best to keep control of the board and just keep whittling them down.  Try to combo your Sunkeeper with muster or vinecleaver.  Shaman is probably the hardest match up because Devolve wrecks this deck. 

I waited until after the Warleader nerf to post this deck just to make sure it still works. While the nerf definitely hurts in some situations, I've gone from rank 5 to 3 after the nerf with only a few losses, so it's still good!

Good luck! With so many priest right now, this is an easy climber!