Apparently I either was lucky or the Warrior class is by far the easiest, because I tried the Fire Mage next and it was a lot harder.
My Warrior had a lot of defence, allowing him to outright block probably more than half the attacks and ignore about half the damage on the attacks that came through, while having a massive health pool, a regular and an AoE attack that push enemies back, a charge attack that lets him get to ranged attackers and self-healing.
My Fire Mage on the other hand has very few options to avoid getting hit. They have a small health pool, rely on ranged attacks that have a shorter range than most ranged attackers, have one conditional short distance teleport that uses mana and their summons die within one or two turns doing very little damage. And once you're out of mana you're pretty much screwed, as it regenerates too slowly when you really need it.
I tried a Necromancer which went a lot better, as he has some life steal abilities, but then I had to go through a dungeon full of enemies which were resistant to toxic damage, which is the damage type of all Necromancer spells. My Warrior had a weapon that ignored armour, so he never had to worry about being less effective against specific enemies, but it seems Mage classes don't get something similar. You can learn spells from other classes if you find them, but in all my runs I wasn't able to properly prepare for enemies that were resistant to my main damage type.