Oddly enough I'd keep them in shoe boxes over a plastic container such as a large bin or one of those plastic sealed type containers. My reasoning is pending on where you store your coins, if moisture is present when you close the plastic container, it stays there. Evemtually may attack anything you put in there. At least a shoe box can breath so whatever moisture is there when you close the lid, it will still be able to seap out.
Presently all my Proof and Uncird sets are in large cardboard boxes. And have been there for a long, long time. Items I've put in plastic storage containers have in the past warped, tarnished and some leather gun holders turned greenish and fell apart. Since that I've kept coins in cardboard. For 2x2's I use those large, two row, cardboard boxes by Whitman.