Yeah, it does take its time to build up, but in my opinion that just lays a stronger foundation for the latter half(-ish) of the book.

Use of Weapons is more than a decent intro, but I'd still personally recommend The Player of Games since it isn't as deep and heavy in comparison, and the narrative structure is simpler.

Of course, YMMV, but I started with TPoG, and reading UoW right after it was absolutely fantastic. I guess my biggest concern with recommending UoW as the starter would be that it might diminish TPoG, which I'm fond of, but I don't know if it actually would, since they're connected pretty much only bound by the setting.

I've read (in order) Consider Phlebas, Player of Games, Use of Weapons, and Excession thus far. Use of Weapons was the toughest one for me to get through so far. I started it and stopped it a few times over several years and just couldn't get past the halfway point. I eventually got over the hump with it and devour the last half of the book over a couple of days (which is fast for me). So for my money, Use of Weapons is a bad starting point.

My favorite by far is Excession but I don't know that I'd start there. I think the payoff of getting a story from the perspective of the Minds is better appreciated after you've heard about them and their capabilities from a distance in the preceding books.

My pick would be to start with Player of Games. That's the one that was a page turner for me nearly from the jump.