Mulligans
General Mulligans
Against slower decks, you want to be able to ramp and remove larger threats, while drawing the pieces needed for bursting the opponent down.
Aggro Mulligans
Against Aggro you want to have two things: tempo and health gain. Health gain without tempo is useless, as you will continue to take damage if you do not remove the threats on the board. The good thing about this deck is that it can only take two turns to pull a win - building a board then using board buffs to burst an opponent down.
Midrange Mulligans
Against Midrange you are at a larger risk of being flooded as they curve out into larger threats, so you want to be better able to deal with them through ramping faster than against aggro. cards like Violet Teacher and Mulchmuncher are very good at mitigating damage and stealing back tempo and are good counter-threats that need to be dealt with by the opponent.
Combo Mulligans
Use a combination of these cards, especially Violet Teacher followed by multiple spells and finally Soul of the Forest, before finishing with a combination of Power of the Wild, Savage Roar, and Branching Paths.
Control Mulligans
Against Control the win condition is big burst damage from multiple minion buffs on a large board. To ensure this, ramping into draw to set up the combo while maintaining board presence. If you lose the board against most control decks you will be forced to waste combo pieces winning it back.
This deck wins through ramping into Violet Teacher then Soul of the Forest. Following that, minion buffs such as Power of the Wild, Savage Roar, and Branching Paths. Tempo created by cards such as Mulchmuncher and, of course, Ultimate Infestation, helps to stave off defeat while the board state is set up.
Good Luck.