Kind of late with the suggestions, but here`s mine:
Jazz - Toni Morrison: I think that Jazz is a mature experience, but a very rewarding at the same time. Complex and raw, i believe that can give you a great overview of the 20's american society
The name of the Rose - Umberto Eco: A true masterpiece, a mix between science and religion, and a straigth discussion around the man's true nature, it's an amazing book, but requieres a high cultural level
Farenheit 451 - Ray Bradbury - I believe that someone else suggested before, but i can reafirm thhis. A clear dystopia and a reflexion about the importance of the books in our lives, and as a tool to oposite the control of the media.
As a personal commentary: Don't start with the true classics. Start with the XX cent. books and then go backwads. First train your eye and your mind and then go for the big fishes. Enjoy!