My advice is to read both
The Hobbit and
The Fellowship of the Ring immediately before seeing the movies, but then to see the remaining movies first before reading the corresponding books (
The Two Towers,
The Return of the King).
Here's why:
- There is much introductory and expository information in the books that may not come across as clearly in the movies. Most of the essential information of this nature is in The Hobbit and The Fellowship of the Ring.
- By reading at least The Hobbit before seeing the movies, you will have a chance to form your own vision/interpretation of Tolkien/Middle Earth, without outside interference.
- By not reading The Two Towers or The Return of the King before seeing the movies, you will be able to experience that part of the story on film de novo, instead of already knowing the basic plot.