About the best thing you can do is keep it within the climate controlled area of the house. Temperature stays pretty even, and humidity stays low. If you're going to have them where they're subject to more variation (garage, shop, etc...) you definitely want to seal them up and keep them dry.
If you have several cases at a time to store, about 30 gallon size plastic drums with some dessicant are nice. For instance...
http://www.valumotion.com/index.php/cPath/700_4442_790_8957 (open head obviously) That size is still fairly easy to move, something to keep in mind. Ammo is heavy. You might also want double check that what you want to store will fit into the container.
The drums are nice and durable, you can put the open box you're shooting from on top and keep the rest sealed up. If you're keeping them for long term storage you can line several up and lay some plywood across the top to get some use out of the space. The sealing ring is usually lockable too, at least enough to keep curious kids out of it.