I've read in a Amazon review that it is recommended to start with Consider Phlebas, then The Player of Games and finally Use of Weapons (as a first start into the Culture, that is).
I've bought them three myself and will read them in this order.
Use of Weapons is great, but the writing is poorer than the other two.
Heh. Interesting. I'd say exactly the opposite myself. Not that I dislike the other two - PoG is one of my faves of his SF work - but to me UoW is a vastly better work of literature, both in structure and character development. Less full of SFnal goodies than some of his later work, but all the better for that in some ways.
I've bought them three myself and will read them in this order.