Mulligans
General Mulligans
These are generally the cards you want to mulligan for unless you are facing a certain deck type such as zoolock, etc. Acidic swamp ooze can be great at slowing down Midrange Shaman's early game, using to kill spirit claws. Loot Hoarder gives this deck early board presence and card draw and Doomsayer is also great at slowing down aggressive decks. Acolyte is a good turn three used for drawing cards. Truesilver is great at controlling the board into the mid game.
Aggro Mulligans
Barnes is a pretty aggressive pick in my opinion. The earlier you play it the less likely you could pull a larger minion in the late game. Aldor can also be a risky pick depending on whether your opponent is aggressive or more control oriented.
Midrange Mulligans
These cards are the midgame. They help set up some board presence and transition into the later stage of the game where you start pumping out the big threats like Tirion or the Ranaroses. Don't be afraid to sacrifice a Sylvanas to a Hex if you think you can get Tirion to stick on the board. Certain decisions such as this can be crucial to winning or losing tight games.
Control Mulligans
Doomsayer is great for controlling the early game and Equality with Pyromancer is a fantastic board clear. Usually I keep Equality or Pyro/Consecration if I'm facing a very aggressive deck such as zoolock.
Nzoth Priest for the lil homie.