RE: what to do for storage
The important thing is to clean the inside and outside of the barrel real well. If you believe there could be things under the bases of the rifle, then by all means take then off and clean under them. Personally I never do. All my rifles are with quick release rings so they stay in place.
But once I am sure there is no trace of fowling that I can see... On the outside of the rifle I spray it down with Birchwood Casey Sheath a.k.a. Barricade. I let that sit on the outside of the rifle and wipe it off leaving a good solid coat. The inside of the bore, I like to use Sheath or Break Free CLP.
Some people break the rifle down.. ie; remove the bolts, breech plugs, springs so they are not under tension... since I shoot my rifles all year round I do not.
I just started with a product called Montana X-treme Bore Conditioner but like I said, just started and have not formed an opinion on it. One thing that kind of startled me.. I thought the rifle was spotless and yet this stuff pulled some oxidation out of the bore. I never would have guessed that was in there, but that can be the only explanation of the black smudge that came on the patch as I am positive the bore was clean and bright. More to follow on this product.