Some people say "only use water", and they're usually called "the police". I think a bit of alcohol helps. So I have a few shots of whisky and then heavily breathe over the more stubborn spots on the screen. Then wipe with a dry cloth (usually my sleeve). Repeat as needed.
For scrubbing down stacks of Ultrasharps that have been splattered by years of coffee, noddles, soups, and godknowswhat: Can of Maxiclean spray foam, and a microfibre cloth. The Maxiclean is water-based, so the cloth is mandatory to avoid residual water dripping down into the screen when you turn it upright. Isopropyl doesn't do diddly-squat against heavy staining. These are all screens with plastic matt surfaces rather than glass + anti-glare coatings, so YMMV if you have a monitor with a more delicate surface.
Well hîc..., the perceived image quality is only a function of the screen's cleanliness and the alcohol-induced blurry vision. So mix and match the number of whiskey shots with the amount of smearing using your sleeve until you reach the image distortion level that works for you.