CLEAN
Water ... room temp, NEVER warmer to hot!
SOLVENT
If I need to use a solvent, Butch's 'Bore Shine' for black powdah is phenomenal, best I have ever used!
STORAGE
Short-term: Ballistol.
Long-term: Birchwood Casey's 'Barricade' product.
Ultra-Long-term: RIG grease.
I do this and I use black powder.