I'm in agreement with CeJay here. At least if the fan fic writer wants to enjoy themselves more, I think it would behoove them to write in the time period or with the characters they feel most comfortable with. I was a big fan of DS9 and the Dominion War, so I based my Dark Territory series in the post-Dominion War era to exploring what might have happened after DS9 ended. The good thing about that for me was that it also allowed me to also incorporate TNG and VOY into stories as well.
I think you first got to find something that interests you to keep writing when you hit the eventual writer's block or when life gets in the way. But also I do think most people who write want to share what they've written. But if you're not enjoying what you're writing, if you're too worried about the audience, you're probably not going to like what you produce and they probably won't either.