Does it get better in the later chapters?
I know Use of Weapons doesn't depend on any of the other books for its plot, but is it a decent intro to the setting? If it is, that's where I'd recommend starting.
Use of Weapons is more than a decent intro, but I'd still personally recommend The Player of Games since it isn't as deep and heavy in comparison, and the narrative structure is simpler.
Of course, YMMV, but I started with TPoG, and reading UoW right after it was absolutely fantastic. I guess my biggest concern with recommending UoW as the starter would be that it might diminish TPoG, which I'm fond of, but I don't know if it actually would, since they're connected pretty much only bound by the setting.
My favorite by far is Excession but I don't know that I'd start there. I think the payoff of getting a story from the perspective of the Minds is better appreciated after you've heard about them and their capabilities from a distance in the preceding books.
My pick would be to start with Player of Games. That's the one that was a page turner for me nearly from the jump.
I like 80% of his work, 15% is a pointless depressing slog, and the other 5% is just too much for me.
Really, Culture is a great setting for discussing a lot of interesting philosophical questions and topics.
I enjoy the settings and the concept of the Culture more than the plotlines.
