I use CLP or Rem Oil.
I used to use Mpro7 gun cleaner since it's supposedly non-toxic. But I found that it left a sticky residue on my guns, so I stopped using it.
You know those sets of gun brushes that come 3 in a package? Usually one is nylon, one is bronze, and one is stainless steel. I set aside the stainless brush far away from my guns so I don't accidentally use it. I used a stainless brush before, and it took off the bluing.
For any blued gun, I use the nylon brush first. I use the bronze brush on the breechface and on the front of the cylinder if there is carbon or lead buildup that the nylon brush can't remove. I only care about removing the layer of carbon or lead that can bind against the forcing cone. There will be some staining on the front of the cylinder that may not come off. But that's okay because I'll just shoot the gun again next time I go to the range.
I use a bronze bore brush soaked in CLP or Rem Oil to clean the bore and chambers. I follow up with wet 12 gauge sized Hoppes patches. I like the 12 gauge size patches since they're bigger than .38 sized patches. After the wet patches come out clean, I use some dry patches and ensure that I've completely dried the bore and chambers.
An important area to clean is behind the extractor star. The small tip of a nylon brush is good for this. I then use a .22 caliber sized Ramrodz to dry the area under the extractor star.
Something else to consider is not storing blued guns in foam lined cases, since the moisture buildup can cause rust.