Normaly water is is good to clean the monitor with. But to get off greasy finger prints and the like a cleaner is good. BUT! Do NOT!! use any cleaner with Ammonia or Isopropl alcohol. And those cleaners with the harsh chemicals I wouldn't use with a screen with anti-glare coat.
The best and cheap thing to use that is PERFECTLY safe, is "Glass Plus..glass and surface cleaner". You can also get this at any grocery, or drug store. Use this and and this alone.
It contains No ammonia or alcohol or phosphates. Here are the ingredients in total.
INGREDIENTS: Biodegradable cleaning agents (Surfacants), Fragrance, and Water.
This stuff is AWESOME! And perfectly safe. It's great on a keyboard and mouse too. I just spray a bit on a cloth or papertowel and wipe down the keyboard and mouse, including each key.