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…
Favorite ship name is an impossible choice. There’s so many and they’re all so good.
The one that most easily comes to mind is the Mistake Not… but you’ll have to read Hydrogen Sonata to hear the rest of the name and understand why it’s so good (I ain’t spoiling that reveal).
But in terms of just random names that get offhand mentioned, I always found Prosthetic Conscience delightful.