For Mario I'd do a Dwarf Fighter or Barbarian (something Str-based for big jumps) using a Warhammer and thrown barrels. There's probably a way to weaponize your jumps in this game too but I haven't looked into it, so I'd go old-school DK Jumpman.

Peach is tricky because her videogame portrayals have varied wildly. Sometimes she's known for healing and singing, sometimes for flight, sometimes for throwing things, sometimes for... ugh... weaponizing her emotions. I'd probably go for some flavor of Bard or Sorcerer.

For Bowser I'd probably do a Dragonborn Vengeance Draconic Sorcadin, with some mix of green and red to get the look and the fire breath, with plate armor serving as the shell.
How's Mario going to use fire if he's a Fighter or Barbarian?