Most of my life I cleaned my guns in a baking tray on a board sitting across the top of a half-barrel of diesel oil or kerosene. Now I use an old mechanics fender cover laid on my bench with the end of the barrel in a cut-down 8# powder jug to catch the drainage.
I prefer to hold the gun by hand and put the muzzle into a plastic bucket to catch the runoff and spatter. Especially when cleaning blackpowder cartridge guns.
I have a holder similar to what MTA Tom has, but seldom use it for cleaning. Many of these types of holders either hold the gun horizontally or worse sloping towards the breech, allowing gunk to drain back into the action. This is especially a problem with blackpowder cartridge guns. If you get a gun holder, make sure it will slope the gun down towards the muzzle.
I purchased a set of "rubber" pads, designed to hold the barrel from a vendor at the Southern Grand about 3 years ago. I paid $35 for them and kept telling myself, as I headed home, how foolish I was to spend so much money for pads.
Three years later, and the pads are still perfect (unlike two others I bought earlier for a lot less money) and they hold the barrel very solidly yet leave no marks.