DIAGNOSIS You're right to be careful. The screen has an anti-glare coating that harsh chemicals will strip right off, leaving permanent smears.
FIX Power it off. Dampen a soft, lint-free microfiber cloth (like for glasses) with just water. Wipe gently in circles. For stubborn spots, a tiny bit of distilled water or a screen cleaner specifically labeled as safe for anti-glare/matte coatings can help.
IF THAT DIDN'T WORK For adhesive residue (like from a sticker), a tiny drop of isopropyl alcohol (70% or less) on the cloth, not directly on the screen, can work. Test on a corner first and wipe the area with water afterward to remove any alcohol residue.
HEADS UP Never use window cleaner, ammonia, bleach, or abrasive cloths. Never spray liquid directly onto the screen—it can seep into the edges and damage the internals.