It might also help to check out other good fanfic authors, (and there are very few). But I do recomend
"The Jewel of Brandy Hall". What happens in this story is very implausible but the way in which it was written makes it seem almost like you could believe it. It focuses on the first believable descendent of Frodo Baggins that I have ever seen. And the author makes good use of her knowledge of Tolkien's writing style and his characters. It's long but worth the trouble.