Usually I would recommended plastic boxes as long as they air tight.
But a new method is to use the vacumn plastic storage bags usually used for storing clothes.
They are readily available from stores like Argos though I've also seen them in Pound Shops and other low priced retailers.
In case you haven't seen them you put the items in the bag and then 'deflate' them with a vacumn cleaner. The bag shrinks and forms a solid airtight package. You would be able to store lots of paper in them and could put five or six bags into a plastic storgae bag for extra protection.
