To store my armies and work in progress, as well as transport them for gaming, I use clear plastic storage containers. Each case holds 270 infantry or 108 cavalry. I buy them in batches from a local hypermarket, trying to get as many of the same design as I can. Unfortunately they keep changing the design. The large ones are 32 quart / 30 litre Sterilite or similar Rubbermaid ones. Look for ones that have square-ish cormers, they won't be perfect but it avoids a dead zone. I also use a series of smaller ones, again by Sterilite, that come in a couple of different depths, a 6.2 qt / 5.9 l and it's double depth cousin.
None of the storage boxes come with a flat bottom for strength reasons. I put a sheet of foamboard inside to make it flat, cardboard or styrene sheet also works. Just cut it to size, clip the corners and drop it in. I buy black foamboard in bulk (search the web).
I then put magnetic sheet on top of the foamboard, the sheet comes in rolls from sign maker suppliers.
Miniatures are then stored on magnetic movement trays, or directly on the sheets. All my minaitures and trays use magnets, originally metal plates, but now Litko flexsteel and flex magnet precut bases make the job easier, together with 3/32 x 1/4 rare earth magnet superglued under the plastic bases (and then covered with Litko flexsteel.