I read them in published order, starting with Consider Phlebas, and I have no regrets. But if I only had one book to convince someone the series was worth it, it would probably be Player of Games. Did you enter somewhere else?

I'm pretty sure I read Look to Windward without realizing there was an entire series of books set in the universe. Excellent book, I ploughed through the rest of them shortly after. I'd definitely recommend starting with Player of Games, most folks like it more than Consider Phlebas and I found Phlebas a bit weak compared to the rest of the series.