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 am reading them in published order as well though I’m not 100% sure I will continue with the series. So far, it doesn’t hold a candle to The Expanse series or the Inhibitor series.
I really disliked the deus ex machina endings of Consider Phlebas and the Player of Games.
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.