Actually, thinking on it some more, I think maybe the gear system as it currently exists is closer to what you want than you might think. If what you're looking for is letting the characters have some small number of "things" without regard to what the "things" are or how they compare to other "things", then maybe what you want is to just use the current system but ignore gear calibers. That way a character gets ~2 items from their charisma, and 0-16 or so items in specific categories from their class, depending on specific class and level, and maybe some personal possessions in addition to that. And that's it. If you also want to make up some bundle items in addition to the individual gear that already exists and have the bundles cost more than 1 pick, that could speed up the process of getting gear. You would just have to make sure that the bundles are obviously better than any single item, otherwise players will agonize over whether the bundle is worth it.
If you're so inclined, you could also say that items of a certain caliber cost 2 picks, or from certain categories, like tactical weapons.