Mulligans
General Mulligans
See Aggro and Control for more explanations.
Aggro Mulligans
Usually you want to look for cheap removal spells mostly, but Volcanic+Bloodmage Thalnos is a great play vs token decks, and tar creeper can be worth holding on too if you have a 1/2 cost card ready or are on the coin.
Control Mulligans
Vs control you want to be holding on the any card and value generation on top of normal early game, and ofc the mvp: Frost Lich Jaina.
With the lategame value and heal from Frost Lich Jaina, a midrange version elemental mage should be viable. Elementals give you had and board value, while keeping up tempo with most decks. Then once Frost Lich Jaina hits the board, the value of heal from the lifesteal buffs and a free Water Elemental here and there, should make this deck survive both control and obliterate aggro.
Baron combo with Drakkari Enchanter can be considered, but i think its too much setup for a deck that already has a lot of tempo. Baron alone might be a better fit if there is a lot of token decks, but at the moment i will rather have cheaper minions, and save the 7+ for Jaina and 2x Blazecallers. Also you could replace Igneous Elemental with Fire Fly.