Use of Weapons is the second Culture I'd read. Player of Games introduces the Culture as a whole better.
That's the order that I read the books in also, and I agree. I think I liked Player of Games better than Use of Weapons, and not just because of the ending.
That's also the order in which I read them, and the order of relative publication, but I wouldn't ever recommend anyone to start listening to the Beatles from their first album, say. I'd start with the one I think they'd enjoy reading the most. Plus, he actually has a copy of Use of Weapons, so he should just jump in rather than wait 'til he gets a copy of Player of Games first.
THAT SAID, Player of Games is a lot more approachable, plot-wise. Use of Weapons is a bit of a headfuck.
I've started on The Girl with the Dragon Tattoo. Deathly dull so far but I can only hope it picks up. My current 'toilet book' is Bob Dylan's Chronicles, which is so awesome I may promote it to 'train book' status.