Hearthpwn

As of updating this, this deck has a 27-10 winrate in diamond 5 or so near legend. Cards like Ramming Mount and Doggie Biscuit give you favorable early game trades into board based decks, like pirate warrior, secret paladin and token druid. and against more combo type decks, your ability to make a wide a resilient board through eggs, pythons or acolyte is often too much for them to handle if you can get it going fast enough. and even into more control style decks, cards like tonk and jewel of nzoth give you many waves of threats for them to try and fail to deal with. The warsong wrangler also serves as a great way to fetch and buff very key cards such as the lion and the parrot, which are massive tools to swing the board back or mount up pressure. 

For the mulligan guide:

Against decks that try and win by using a swarm of minions in the early game to overwhelm you, devouring swarm, carrion studies, and any of the 3 or less cost deathrattle cards are very good. If you already have a deathrattle, lion is also worth considering keeping against these decks.Ramming mount has also solo carried me to victory especially against druids.

Against combo decks like mages, and garrote rouge, this is a tough matchup, so your best way of winning is popping an egg or python and then copying the deathrattle with lion or parrot and then smorcing the opponent down.

Against control/slower type decks, this is why the acolyte is in the deck, spend time thinking about when you want the deathrattle to be activated, then take advantage or your syngergy cards like swarm and parrot to create a ridiculous board. in my experience this is the best way to beat decks like big warrior, and any slower priest or druid decks. Also, in slower matchups, be careful about playing worse deathrattles so your jewel can be more consistent. 

Tonk is the ace up your sleeve to close out games. If they kill it, it either helps clear their board or finish up damaging their face, and then you can use parrot to repeat the death rattle for massive amount of burst.

You could also consider cutting one deaths head cultist for a zixor or a teron, but in my experience its not needed.