How About Putting on Some Gloves, Jack

Buyers have better eyesight than sellers
1934 Lincoln Cent, MS63

I will use a cotton towel to lightly wipe society's grimes off a coin. Once, ok. Twice is pushing it. At 3 times, you are polishing it.
This is the most cleaning I will offer a coin.
I wiped a small bit of debris from a proof cent...one swipe...RUINED IT.
For brown, circulated coins I have no problem handling them with my bare hands. That's why I choose to work with them most.  For BU rolls and proof coins, I've learned the hard way to put on gloves.  It only takes one light touch to leave a fingerprint on a coin.  Add some combindation of warmth, humidity and time, the skin oils and perspiration will darken, leaving the most unsightly mark on your otherwise spotless coin.
Cotton gloves are available online or at your nearest pharmacy for less than $5.
Latex gloves are cheaper, 50 pair for 5 bucks, available at walmart.
Use them once, save a $5 proof coin, it pays for itself.
Cotton can be washed, not a bad idea seeing how filthy they get even when used for BU coins. Just be sure to rinse the bejesus out of them or the detergents can cross-contaminate the surfaces you are trying to protect.

Even when wearing cotton or latex gloves, try real hard not to swipe your finger across the surface of the coin. Particles and grime can stick to the gloves just as easily as your fingers.

Make the investment.  It's 5 bucks.  You probably spend 10-100 times that on your phone.

If you choose not to wear gloves when handling BU, Proof, or extremely rare/valuable coins, the entire numismatic community would appreciate if you also chose to get involved in a different hobby.  Try cooking.

 I've added a video to go along with this article.