With what should I clean the screen of my Macbook mid-2010 White unibody?
If you need to clean your Apple hardware use a clean dry microfiber cloth. It's what I see Apple employes using on all the equipment in the Apple stores. I've been using microfiber for years on all my Apple devices and has worked great without any damage.

Note: If necessary you can slightly dampen it with distilled water and wring it out well so it is really just ever so slightly dampened and the follow up with a clean dry microfiber cloth.