For medium or long-term storage I would highly recommend buying some mylar or poly (polyethylene or polypropylene) sleeves for keeping your posters in. These not only prevent mild accidental surface damage such as finger prints or scratches, but also provide an inert acid-free environment for your poster thus reducing any potential paper degradation. They are ideal for flat, rolled or folded posters.
Protective sleeves come in a variety of sizes and materials, with prices to match. There are two main materials that you'll come across:
Personally I'd say that if money permits then always go for Mylar, mainly because it offers that little bit extra in terms of protection, and displays the posters / lobby cards inside perfectly. Having said that, high quality Polyethylene sleeves are more than adequate for most uses, so the decision really is up to you.
|Lobby card display book|
If you've bought your sleeves then you'll probably realise that with a sheet of paper inside they're not the most sturdy storage medium in the world. With Mylar especially it's best to keep the sleeves flat, which makes handling difficult when you're dealing with a 41"x27" sleeve. The best solution is to buy some archival safe backing boards to go inside the sleeves to support the poster.
|"Deliverance" UK Quad in a Mylar sleeve||Mylar and backing board|
Considering your posters will be in direct contact with these boards then it's worth investing in acid-free or archival safe backing boards. Using ordinary sheet cardboard is not recommended. Acid-free or buffered board will not only never affect the poster itself but will also be able to neutralise any acids that it comes into contact with.
You can buy specialist acid-free boards from a few online retailers, but a cheaper alternative is find a good local frame store that can provide sheet matting / mount board that's normally used for framing posters and pictures. Conservation mount board, even 1-sheet size, can be had fairly cheaply and is ideal for poster storage. It can even be obtained in a range of colours which is handy for display purposes.