Mulligans
General Mulligans
Always keep Mana Wyrm, Frostbolt, and Arcanologist. Medivh's Valet is also often a good keep but less than the previous. If you think you're against aggro, keep Volcanic Potion. If you have no better early drops, keep Babbling Book . If you already have Mana Wyrm Primordial Glyph is a consideration.
This is an example of a pretty standard, popular, Burn Mage deck one might see on the ladder as of July 2017, Season 40. It is the list used as the target example in Switters’ Anti-Guide for Burn Mage article.