Instead of using the wet wipes that are meant for your hands, head to the nearest optician and get a pack of pre-moistened lens cleaners. They won't leave any residue and do a good job.

That plus a large (8"x8") lint-free eyeglass cleaning cloth I snagged at a dollar store keeps all my screens clean. I put the lint-free cloth on top of my keyboard before I close the screen, to try and prevent the keyboard from leaving marks on the screen.