I wonder what kind of Fan Fiction to write...

Well, if you're a new Fan fiction author, I'd suggest picking the Quelle material you're most familiar with, and Schreiben about it in canon style. It's simpler than alternate character interpretations, OCs, AUs, and anything else deviating (radically oder otherwise) from the original source. It's also likely to garner less hate, even if it isn't incredibly original. Just don't rip off an existing episode.