Never clean a coin until you know what it is, and what it is potentially worth. I have a tumbler but only use it for clad.
The first thing I do is make a determination if its a valuable coin I plan on selling someday or just a coin I want for my collection. If it's one I plan on selling then just mild soap and water.
For coins I plan on keeping such as large cents and old coppers - first I rinse in soap and water and use a soft toothbrush to get the dirt off. Then I soak them in Hydrogen peroxide for a day, I change the solution a few times. After the peroxide bath I gently scrape the now dried crud off the coin surface with a toothpick, be careful,and take your time. Then I cover the coin in petroleum jelly and work it in and let it sit for a day. Lastly with a soft cloth I rub off the petroleum jelly which usually removes the last of any dirt.
For old silvers I just use mild soap and water, if it's a barber, mercury, rosie or seated with mintage in the millions (ones that aren't worth much.) I use a soft toothbrush with dishsoap, then wet the coin and dip it in baking soda, work the baking soda in with your thumbs and that coin will shine like a mirror.
The pics below show a large cent as it looked out of the ground, and then how it looks after the soap and water, soft toothbrush, peroxide, toothpick, and vaseline cleaning method. This is just a method of cleaning my buddy and I use, I'm sure there are many that would disagree with it, but to each his own.