Of course you are not a true lord of the rings fan if you only like the movies. I mean The LOTR movies are pretty much as any action/adventure movie but with orchs, wizards and hobbits
And with this I am not saying that the movies are bad, quiet the opposite they are good, very good!
but if you reallly really....are a true Lord of the rings fan you should be interested in more literatur of Tolkien than the trilogy.
Booklist for a true fan to read.
1. The hobbit
2. The trilogy ( of course )
3. The silmarillon (gives you important history facts and the most important how middlearth was created )
4. The unfinished tales
5. The book of lost tales (1 and2)
But you do not only have to read the books one time but several times ( Like I have) to truly understand the world of middlearth and the various cultures that exists.
But of course everybody can read the books......the most important think is of course that you ENJOY what you are reading, just like Rilwen Gamgee wrote before.