For my 12 and 20g guns I use a bronze brush screwed into the end of one of those fuzzy bore rods. I spray some Rem lube oil down the bore and run the rod thru half a dozen times. I wipe the outside of the gun with the same lube. I lube the hinges with some Mobil 1 automotive chassis lube (cause I have it in large quantity) that I keep in a small syringe.

I never use a lead bore removing solution. My feeling is that it will definitely get on the muzzle area around the rib and wick up the solder line a ways. This type of chemical is designed to desolve lead. Lead is one of the primary metals in the solder that holds the rib on and the barrels together. Enough years of this, and I believe these type of chemicals will cause the rib solder joint to fail.