I would suggest the book first. First, because a film provides one interpretation of the book(often a merging of the director's and author's vision). In a discussion among readers, a wealth of perspectives can be shared because of a book's ability to engage the reader on a personal level through imagination. The same might be said of a film, but the visual aspect plays strongly on the mind too, somewhat diminishing what the mind imagines. Second, seeing the film first might spoil the experience of a book!
Lord of the Rings is a good example. Despite the monumental achievement of the films, a first-time reader of Tolkien introduced to middle-earth through the movies would find it difficult to imagine the characters without the faces of the film's cast. Our frequent exposure to LOTR via social media, etc., might create too much familiarity to truly engage with the book's story. Of course Tolkien's world is nigh inexhaustible, so even though I was introduced to the LOTR films first as a child(which upsets me somewhat), I will continue reading this fantasy masterpiece
So in summary, book first. Your experience will be enriched by how you engage with the novel personally
This was just one example, but thought it might clarify best that way. Plus Tolkien is the bomb of world-builders. Ok, monologue through