Mulligans
General Mulligans
Shimmerfly because it's a good dude to just get the value rolling, Ursatron to draw your other mechs, Animal Companion because Animal Companion, and Shaw is just too good to pass up. Any other choices are up to you.
Aggro Mulligans
In aggro you're just looking to survive, which means you want things able to remove stuff, get you more things, and do double-duty by rushing your deathrattles into active minions to get more stuff and kill other things.
Midrange Mulligans
Board control is key here, and being able to both control the board and advance your gameplan through winning the value game (Marked Shot) or doubling up the threats (spider bomb) makes for a winning strategy.
Combo Mulligans
Kill, kill, kill. This is not a suggested opening hand; these are the cards you WANT TO DRAW to create resilient boards that are a pain to clear for your opponent. They will be dedicated entirely to keeping you alive, so these cards are the ones you want to see in order to pressure them down.