I'd suggest Player of Games first; I found it better as an introduction to the Culture. They're not really a series as such; his Culture novels share a setting but don't share any characters (well, almost none) or any particular plot continuity, so you certainly don't have to read them in order.

I'd suggest PoG as a starting point to explain what the Culture's about, which I think it does better than CP because the main character in that is not of the Culture. YMMV though.