Mulligans
General Mulligans
Try to find the low-cost cards as early as possible, as that's when they have the most use. Besides that, Oaken Summons and the Whomper are two really key cards.
Aggro Mulligans
The eagle token(s) and Korrak can hopefully stave off some early minions, and the Shellfish might be a big enough target for them to trade into.
Midrange Mulligans
You need to be able to both control their board and enact your own value plans.
Combo Mulligans
Against Combo, you'll want to mill as much as you can, and on the off chance that your opponent really needs some Dragons for their combo, Grapplesniper might actually get a good hit off of both players. Elysiana is for when their combo involves bombs, corrupted bloods, or the like.