Good luck to them when they get to Surface Detail!
Lots of good stories and setups to draw on, but I wonder how the vanishingly low number of recurring characters would handled. Incidentally I think Consider Phlebas is a good starting point for a TV show - even if it's far from the best if the books, it creates the opportunity to introduce the Culture from the PoV of an engaging outsider and opponent, while still retaining all its mystery. Also, galactic-scale space war, and one of only two major 'historical events' in the series, acting as a bit of an chronological anchor in an (apparently) unchanging world.
Namewise they should just call the series Special Circumstances.