Agree with the others Rem Oil is suspect. But you could thin it with Kroil and it would be alright for cleaning. Corrosion X and Ezox have worked well for rust protection. Will try Frog Lube and Hornaday 1 shot next time I stock up.
The concoctions work well for carbon fouling, Ed's Red, or ATF, STP, with either Kroil or Mystery Oil all work. Not brave enough to pour Mr. Clean Amonia down the barrel when there are so many good products out there for copper.
Bear grease is for the saddles and black powder patches.