This how I clean after regular use. Caliber specific. With help from a rag and a small brush. Once a year or so I tear them down. The Winchester are a bigger PIA than the Marlins to tear down.Or could buy one of those bore snakes ( otis ? ) and clean from the chamber.
A friend once showed me to put an empty casing in the chamber. So when you cleaned from the muzzle end, the crud fell into the casing.