I have a roll of the chux clothes I got from Costco..so it's huge! I use those for things like cleaning my toilets, bathrooms, cat stuff and throw them out after each use.
I use the Vileda Naturals clothes (green) for dishes in the sink that don't need a scourer (we also have a dishwasher) and wiping down my benches or stove top.
You could disinfect them in something like Pine O Clean, I haven't seen the need as I just throw them away when they get a slimy feel about them or I think it's need to be thrown out.
I also have a scotch brite the ones with scourer on one side and sponge on the other I keep at the sink as well as the Vileda to clean the more difficult pots and pans I don't put in the dishwasher (again I bought the scotch brite in bulk from Costco).