Mulligans
General Mulligans
SPIRIT OF THE DEAD you can stuff your deck with 1 cost versions of these powerful cards. Trade often with your opponent while Spirit of the Dead is on board to enable this. You can also buff Spirit of the Dead (or make a copy) to make it last longer.
CATRINA MUERTE she resurrects cards that died. I usually play her on turn 10 (if possible) with seance to get a copy of her. If Convincing Infiltrator has died in this game it's even more annoying.
CONVINCING INFILTRATOR - probably one of the most powerful cards for priest - this is similar to Obsidian Statue, but at a much cheaper mana cost. This is especially great to block big minions like a Mountain Giant. Doesn't work so well against token decks.
ZEREK'S CLONING GALLERY - Get copies of all your minions out, even if they're easily cleared, they are now ready to be resurrected by Mass Resurrection and Catrina Muerte.
Aggro Mulligans
Holy Nova and Mass Hysteria are great to play against token aggro decks like Murloc Shaman, Mech Hunter or token druids.