You can find a full list of Classes here , with details and associated mechanics. Only First-Party classes are accepted.
Gunslinger and all associated firearms/grit mechanics are out, unless someone can give me a compelling reason (i.e. an awesome character concept) to include it.
Summoners are also out, because they're f'ing broken. Again, give me an awesome character concept and we can work something out.
If you can cast spells of any kind, you can use Words of Power . Basically, you trade in potency for flexibility. You essentially 'create' spells from first principles instead of executing existing spells you've learned/memorized/acquired. Particularly useful for immediate casters like sorcerers.
Every accepted class can be customized thematically (skinned), as long as the mechanics remain mostly the same (e.g. swapping out the type of animal your pet is, assuming it's a similar animal).