What kind of character graphics will you be overhauling? For me, personally, I like the style of most of the characters (although I do think the main character could use more customizability).
As for mutations, unless they are high fantasy with multiple distinct races of humanoids to chose from, they tend to be event based - as in, you interact with the game in a certain way as to gain the mutation, like being bitten by a werewolf or interacting with a cursed items. Mutations like this can range from being straight upgrades (think getting a sci-fi doctor to upgrade your body) through having some positive qualities but also negative things (things like vampirism giving you strong abilities but the sun will hurt you and other NPCS might turn against you), or just be straight up something negative you usually want to get rid of like a zombie plague or even just magic sicknesses which mutate your body in odd ways.
Idk if you've already considered that options but I have seen it in a bunch of games and I think it works well.