My iPad screen is constantly plagued by finger prints. I used to clean with a cloth and keep it maticulously clean, but 5 mins later it was covered again.
Now, I don't care. Haven't cleaned the screen in months. I don't notice any more and don't let it bother me. It doesn't effect the use or usability.
In my opinion the best method here is just to ignore mucky finger prints and learn to live with them.