All officially published classes are allowed from the PHB and Xanathar’s. Unearthed Arcana and other homebrews might be allowed but require DM approval first. Don’t feel shy about coming forward with some homebrewed classes
“Fixes” that can be operated on spells and abilities in order to make some subclasses more attractive if you’re willing to look into it. I’m open to discuss those changes that are needed in order for your character to be as cool as you want them to be.
Examples of changes to classes or spells are things like: arcane shots for fighters, witch bolt or crown of madness action economy issues, bumping up some spell damage but reducing it in other aspects, sun soul monk undertuning issues and so on.