Personally the only part of their culture that would seem appropriate to me is the training and war aspects. Yes predators have little predators and somehow care for them, but there are simply too many ways to turn that into a completely un-needed, ridiculous mess. (Not that I expect the people at Fox or any future AVP director to think that aspect is necessary, just sayin. it could happen.) I don't mind a few quick shots of the homeworld though, as long as its nothing too wacky and as long as they don't waste any time making connections to other movies or our own culture, it should be fine.
Personally, I've always wanted a Pred movie that is primarily about how a hunting party or particular clan works. On the ship, in training, during a hunt, blah blah etc. This type of concept is probably way too involved to work and I think most of the people who would see the movie would probably be like, wtf is with the culture ****

, that kind of stuff is generally extra crap that the die hard fans *ahem...us* would like to see. So it would probably never happen, and that might be best. Cause they're sure to screw it up in one way or another.
But if Predator 3 ever does happen, I'd like to see the possibility of more than one predator, a story with a really strong ..."intimate" type of bond if you will, between the characters of the hunting party. But to play it safe and to stay consistent with the previous films, it would most likely just be one lone pred.
ah hell, who am I kidding. they should just make a movie based off the damn comics and novels.