Well... I don't think writing a fanfic is a good idea unless you already have an idea personally, and forcing an idea is never a good idea. If I were you, I'd just keep the whole possibility of writing in the back of my head and then just wait for inspiration to hit by itself. Unless an idea hits you naturally, there's really not much of a point forcing an idea out.
Secondly, when you do decide to write something, I recommend that you consider jokes to be of lesser importance than character, plot and originality, yet at the same time, don't disregard them entirely. A good writer should be able to come up with jokes when writing scenes. Remember, a joke should blend in with storyline and character, not the otherway around.
Other than that, just try to write for yourself and not others. Write the story as if it were a story you'd like to read yourself, make it your own but still make sure it has an overall feel of the show. Good luck