I tried reading the books when I was young-ish, and although I thought them rather cool, I never really got into them, and gave up half way. The main reason was that I was just too confused! The books are not all that fast-paced, and there was SO much going on, and really SO many different characters and species, that I couldn't really keep track of anything, and hence didn't really appreciate it.
So I consider myself to have really seen the films first. And it totally changed my view of the books! I didn't see the films until quite a few years after they all came out, hence I saw them all in quick succession. I was so enthralled by the world that was portrayed, that I wanted to 1) see exactly how the author actually portrayed the events/characters/world of M.E. and 2) just find out more about M.E., and see if the book held any more details than the films. Both of these I found completely in the books, and I consequently swallowed up the Trilogy, then hunted down the Silmarillion, Children of Hurin, several thousand 'guides to middle earth', atlases and what have you, and am now starting the entire History of M.E.! All of this as a result of the films. [

] Seeing places and people on screen, really made it easier to appreciate what was going on in the books. As I said earlier, when I first tried reading them, there were just too many characters, and I couldn't remember who all of them were, because I didn't really 'know' them well enough. From seeing the films, characters have a much more distinct identity, so I found that all a lot more easy to digest afterwards. It was also hard beforehand to appreciate what elves, dwarves, hobbits and orcs really looked like, and acted like. It was all so new to me, basically! Now I have a better idea of all this, and in addition, it helps to visualise in my head the places and people that aren't even in the films
What I am particularly pleased about, is that the film hasn't totally 'taken over' middle earth in my imagination. By that I mean that although the film has shown many of the places and people in LOTR, I can still make up how things look myself.