I have a hard and fast rule: always read the books first. Especially important in LOTR, as you will get a very flawed view of several characters (Frodo, Aragorn, Gimli, Elrond and Faramir are waaaaay off base) and this will change your view of the story. Other characters are bang on (Gandalf was brilliantly perfect, as are Bilbo, Sam, and Merry and Pippin. Legolas wasn't bad. Galadriel was just as I'd imagined.) It is too bad that Gimli was ascribed the role of comic relief. He was much more respectable, and still funny, in the books.
I have read the books the better part of ten times. Start with The Hobbit. It sets the stage, and is a really easy read (it is a children's story, after all). Then, dive into the LOTR books, and let the ancientness of the story take you away. It was written in a different time, and it shows, so don't carry modern expectations into it.
Then, get the blue ray director's versions of the film, and see how long you can stay awake.