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

Well, if you're a new Фан fiction author, I'd suggest picking the Источник material you're most familiar with, and Письмо about it in canon style. It's simpler than alternate character interpretations, OCs, AUs, and anything else deviating (radically или 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.