I fish a ton of jigs on the river. Mostly Precision heads from Bfishntackle by the way. I think the best way I have found is to leave them in the bags they come in if you order from bfishn. Or get some small resealable bags and put your jigs in there. Then I just use plano boxes or tackle logic boxes that are more or less plano boxes. I think the best piece of advice i can offer for keeping jigs in good shape is only carry with you what you are going to need for the day.
If you are fishing the mississippi below the lock and dams that can be quite a few if you are vertical jigging. Keeping a small amount in the boxes keeps the heads in better shape but more importantly it keeps the hooks sharp. The less time jig heads spend getting banged around in boxes the sharper the hooks will stay.
That being said I still find myself with a full tackle bag of just boxes of jig heads. There are just to many different sizes and colors of heads out there now . However I never want to be without something that the fish are going to bite on that particular day.