Zoolock has been a deck since the beggining of time but it hasn't been tier 1 for a while. Thanks to the new 1 drop Kobold Librarian and 2 drop Vulgar Homunculus from KaC I think it is going to be a very cheap and tier 1 aggro deck that focuses more on overstated demons and demon synergy rather than turn 2 Prince Keleseth draws making the deck much more consistant.
The mulligan is going to be almost the same against all classes, keep everything that costs 1 mana and Vulgar Homunculus. If you have a 1-cost demon that you think will survive keeping Demonfire is usually a good idea also. Against rogue keeping Flame Imp can be bad if you have other one drops but otherwise you always keep it.
This version of zoo is very aggressive and can easily win games by turn 5. Push as much damage as possible early game and only make trades you think are necessary. Rely on Doomguard and Soulfire to finish the game. Don't worry about your health total dealing 10+ damage to yourself is fine even if it looks scary you should still make the play that puts the most stats on the board. Make sure to play around enemy board clears (ex: don't make your entire board have 5 health against priest on turn 6).
Remember this deck is not fully optimized so any changes you think you should make you should probably make, maybe even leave a comment of what you changed. Have fun with this deck and good luck on ladder.
Here's a video of Kadak playing the deck: