I wouldn't recommend starting with Use of Weapons - it is probably the best Culture novel but it took me a few readings to really appreciate it.
Edit: As far as I recall, Banks originally created the Culture as a background for the protagonist of UoW - the ultimate warrior:
"The method was that taking and bending of materials and people to one purpose, the outlook that everything could be used in the fight; that nothing could be excluded, that everything was a weapon, and the ability to handle those weapons, to find them and choose which one to aim and fire; that talent, that ability, that use of weapons."
Player of Games was the first Culture novel I read and I enjoyed it a lot. I still sometimes go back and reread it and have found new perspectives each time. Would definitely recommend.
I enjoyed Player of Games and it was a good second book for me after Consider Phlebas. I’ve heard a lot of good things about Use of Weapons, but I haven’t been able to get into it after starting and restarting a couple times.
Edit: As far as I recall, Banks originally created the Culture as a background for the protagonist of UoW - the ultimate warrior:
"The method was that taking and bending of materials and people to one purpose, the outlook that everything could be used in the fight; that nothing could be excluded, that everything was a weapon, and the ability to handle those weapons, to find them and choose which one to aim and fire; that talent, that ability, that use of weapons."