It seems I've read several of the Culture novels, but apparently not in the right order, and apparently not including the first one. Until now.
The first Culture novel, is strange in that it's not really about the Culture at all. Instead it's a story set on the outskirts of an ongoing Culture war. Horza, the main character and more or less hero, doesn't really believe in either side but he's anti-culture and therefore he fights for the other side. The book provides a good explanation though of Culture culture, albeit from the point of view of somebody who stands against those principles and behaviours. It also provides an introduction to one of the main recurring themes of later Culture novels which are the AI run ships that choose their own names.