I keep nothing in cardboard boxes. Everything goes into air tight plastic containers. Ziplock bags are good because they can be compressed or at least the air released out of them. Several can go into AND SHARE a common see-thru plastic container.
One mistake I made ... that I will never repeat... is thinking that the two-piece telescoping containers are air tight. They are not. I had tiny sugar ants crawl up into the the container via the grooves where the top and bottom pieces slide. Maybe if I had put the contents of the container into zip lock bags, I might have been okay...