Humans - no inherent bonuses or flaws. Can do well with anything equippable, though they tend to be better with weapons than magic.
Mutants - Magic, magic, magic! If it’s Magic or a weapon that does magical damage, then a Mutant can use it amazingly well.
Beasts - Human/Mutant + Meat = Beast. They have some natural talents (anything from special attacks to element/status resistances) and can equip items. Not particularly great with weapons or magic, but totally awesome with Martial Arts. The type of beast you are depends on your level and current element, and you will change forms at level up. You may also change forms by eating meat, but sometimes eating meat as a beast leads to…
Monsters - Beast + Meat = Monster. They cannot equip anything other than accessories and magic. Some monsters are good with magic, but never as good as a Mutant. They rely mostly on their natural talents, as they get some talents a Beast will never see. Like Beasts, the form depends on element and level. I honestly don’t like Monsters much in this game, as Beasts also get Talents and can use armor and Martial Arts.
Cyborgs - Human/Mutant + Parts = Cyborg. Cyborgs have basic stats that can only be enhanced by equipping items. They might be able to equip magic (I forget), but unless you really bias yourself towards Wizard-type items that magic is going to suck. Your best bet is to focus on whatever makes the Cyborg’s Talents get better. Cyborgs will also change form based on element and level, but installing more parts might create a…
Robots - Cyborg + Parts = Robot. No magic for Robots. They have some awesome talents, and can equip any items. But the only way their stats go up is by installing capsules. Robots can get very strong very fast if you’re willing to spend the money. They also change forms based on element and level, so installing parts or gaining levels will change your form.
Phew, that’s a lot of info. Here’s my usual party setup:
Arthur - Human. You can always get use from a Human.
Curtis - Beast. Magic + Martial Arts is an awesome combo.
Gloria - Mutant. A Mutant’s Magic power is amazing.
Sharon - Robot. Total powerhouse. She’s your party’s tank.