I've put together a collage of some books from last months What are you Reading? post. It's mostly random, but the more discussion something gets the more it stands out to me. Going forward I'm going to make a new post every month to talk about what people are reading.
I'm on Matter and I'm loving it! Player of Games and Use of Weapons are my favorites in the series so far but I've loved each of them for their own reasons (with the exception of the short story collection State of the Art, it was fine but the rest of the series is on a different level!)
Use of Weapons is great, and comes next in the publishing order.
Consider Phlebias is the first published culture novel and it is a good book. I read it first, but since it gives a more outsider perspective on the culture it probably wasn't best to start with.
Either of those books is my recommendation, although be aware I've only read 4 of the 10 novels. Also as far as I know the books are generally self-contained and can really be read in any order, but there are some references you won't get if you do so.
Excession is my favourite. There's very little cross-over between Culture books, and not all of Iain M Bank's books were set in the Culture (of those, I think I enjoyed The Algebraist the most).
Banks' passing was a huge loss. I don't think there's any other author quite like him.
You might want to go for Consider Phlebas next. Technically you don't have to read them in order as they are self contained stories but there are some overarching aspects that do develop across the books.
That said, Surface Detail was definately my favourite of the series