This $15 screen-cleaning solution is used in Apple stores, and I finally understand why
Whoosh 3.4 fl oz screen cleaner with microfiber cloth removes oils and smudges effectively without alcohol or ammonia, using a double-sided microfiber cloth and milky, non-toxic formula.
Wipe That Sneeze: How to Clean a TV Screen or Computer Monitor
Clean modern screens with a soft, dry microfiber cloth; use distilled water or mild soapy water for stubborn grime, and avoid solvents and excess moisture.