I'll echo that SoBH is pretty great. And the expansions are all pretty good, although I haven't used the expanded campaign rules. They do get a little bit more fiddly, but not much. We haven't done a four player game, but three players games work pretty well. Random initiative each round is the way to go, though.
Also check out their other games - I really like Mutant and Death Ray Guns (which has a new version!) for post
apoc, and it could easily be used for a Necromunda-like game. Flying Lead is good for straight up military/near-future, too. I like MDRG a little better cause its a bit more flavorful.
Edit: also, totally jealous of the Chicago crew. Those are pretty sweet campaigns!