For cleaning I use hot water (not boiling) and scot bright to clean off the fouling, I ram it down the bore with a wooden dowel. I then run a rope down the barrel to pick up and moisture, after a few hours I then hit the outside surfaces with a light coating of baricade oil, and then grease the bore with all purpose gun grease. Salt Silica packets dropped down the bore can prevent moisture build up.
I’ve never really had a major issue with rust build up, if its there I polish it out with high grit Emory and jewelers paper.
One very important thing about my guns I try to keep is being able to remove the breech plug I use a generous amount of anti seize grease to make sure I can without too much work, remove a breech plug.