Just covering the basics:
The Recovery Button is appears on the lower left side of the screen. It's a Green cross looking thing. It restores your HP and Mana to full. You get two recoveries per full rest. You can also use skill points to get extra recoveries to a max of four per full rest.
A Deepfrost Cognac (sold in Wizard towers and other places) sells for 50 gold. It provides 20 mana. Hirge can turn that 20 mana into 125 HP. Just keep her with Heal as her only active skill so she doesn't use mana on non-healing. She'll heal herself and your summons until she's out of mana but you can give her a cognac to have her cast again.
If you're using more than one or two potions per dungeon run, there's room for improvement in how you're using potions. They are best used to stay alive in a fight, not as a way to recovery HP to prolong a dungeon run. In the early game, it's often better to retreat, rest up and try again. That gets you XP, item drops, and saves your gold for equipment, and potions you'll need for boss fights.
As a mage, you might also find summons helpful. The Starting imp lacks durability, but he does keep things off you. Getting a Fire or Ice golem (learned in a wizard tower) will greatly increase your overall toughness.
Mages are well suited from attacking from afar and letting your Companion and your summons take the damage.