Classes determine both the cost of training individual stats and the skills available to a character. Though they are named after and obviously meant to represent the associated character types, classes don't have any IC bearing. That means just because you've selected slayer as your class, doesn't make you a male slayer; you simply have the slayer skill set and training costs. They may or may not affect other things which aren't displayed and difficult to measure such as frequency of autoslays. Note that not all classes are available to all races.
Brute: Brutes specialize in demon buffs and strength, but can also train martial arts fairly inexpensively. Their speed can be trained at a moderate cost on par with a warrior.
Cultist: Cultists are a compromise between magical ability and physical prowess. Their train costs for magical endurance and aligned magic are higher than a witches, but they get a wider variety of physical skills and cheaper physical stats.
Devil: A demon specializing in demon offense and mystic powers. Physical stats are rather costly and unlock a limited skill selection.
Soldier: Soldiers can train physical stats at a moderate cost, but shine when it comes to weapon skill and weapon assembly. Soldiers are the only class besides watcher to have the potential to get the full spectrum of skill and assembly abilities.
Warrior: Warriors are a compromise between devils and brutes, mixing demon buffs and demon offense.
Witch/Sorcerer: Witches are ideal for pure spellcasting characters as they get the full range of magical abilities and can train all of the magical stats cheaply.
Watcher: Watchers get the full range of magic and nearly all ranged skills as well as being able to purchase those stats relatively inexpensively. They also get researching cheaper than any other class.
Slayer: Limited to females in character creation, slayers specialize in physical stats, especially strength and speed.
Fighter: Fighters are meant to represent run of the mill vampires and specialize in physical stats like slayers, especially speed and martial arts. Although they need to pay more for strength, they get martial arts cheaply as brutes and soldiers.