I worried about scratching that plastic screen, polishing it too often. Got a glass screen protector from Amazon, and love it! It still gets fingerprints, but now when I polish it, I don't have to worry about scratches. I think the glass attracts less dust, too.
There are also some anti-static sprays available for computer screens, but I've never found any of them that I tried to work very well. For cleaning, I use Zeiss eyeglass lens cleaner, works great and much less expensive than the bogus fancy screen cleaners. I use the same thing on my 30" computer monitor.