I haven’t read all of Iain M. Banks The Culture series, but I highly recommend Use of Weapons. I’ve read it three times, and it gets better each time.
It’s not a bad introduction to The Culture, but please feel free to recommend another novel to start with, or your favourite. I’ve read this, Look to Windward, Consider Phlebas, and The Player of Games. As I recall, Look to Windward has some good descriptions of a large Culture ship.
I’d also love to hear your favourite ship name.
Edit: I see I added The to the title…
Apart from the fact that every utopia has some aspect of dystopia (IMHO from human nature), I think the Culture series is quite utopistic.