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Cleaning spray for eye glasses works great. Its very mild and intended for glass/plastic surfaces that are coated.
 
I use a SMOOTH microfiber lens cleaning cloth.

If you sneeze on the screen with food in your mouth and let it dry, you might need a water dampened, PLUSH microfiber cloth (like what you might use for cleaning car windows). Then go over it with a dry microfiber cloth.
 
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