I use underbed plastic storage boxes to store the collection. They are made by Sterilite and sell at Target stores for about $8 each. A couple years ago I upgraded from cardboard boxes to plastic after finding mouse droppings in one of the boxes and the boxes shredded.
At first, I lined the plastic boxes with shelf lining, but after while, I realized that the lining was reacting with the styrene Rocos and melting them. Not unlike the vinyl tracks that come with the old Airfix kits that would melt the vehicles over time. So I have been removing the shelf lining as quickly as I can.
I then lay a 14 inch by 30 inch piece of corduroy fabric in the bottom of the box. The shelf lining holds it in place. I use an olive green for American, red brown for German and red for USSR.
It does give a more elegant look to the packed vehicles. The corduroy ribs help keep the vehicles from sliding around inside the box, so they are more organized and don't bang into each other.