I have been cleaning my screens on my Tablet, eReader, cell phone, and monitors with Microfiber Clothe to keep oily fingerprints off them.
You can usually find Microfiber clothe like Microfiber Wonder Cloths ( Set of 4) for a few dollars or more in dollar stores, or online. Microfiber clothes are a lot cheaper then those disposable screen wipes, and screen cleaning kits.
They are also lint free, so you won't have lint on your screen after wiping them like tissue paper, or won't scratch your screen like paper towels which is rougher.
I don't need to use liquids in most cases unless the stain is very oily or dirty like butter, or ketchup.
I recommend using clean water to lightly dampen your clothe to use to clean your screen, and you should never spray or poor water directly onto your screen.
Microfiber clothe can easily soak up finger print stains without liquids when just wiping fingerprint marks on your screens. You can also use them to wipe oils and dirt off your hand.
The clothe is also soft enough, so it won't scratch your screens. The clothe are also very durable, and last for years.
I recommend occasionally cleaning the clothe which you use to wipe your screen to avoid dirt and sand on your clothe from scratching your screen, and to keep the clothe more clean and germ free.
Most clothe are washing machine safe or you can just wash them in your sink.
For a dollar, for a Microfiber clothe, you can clean your screen with the same clothe for years.