Oh man!! There's a can of worms.
Srsly, if you don't plan to shoot any particular gun for years (which is a crying shame; but you make the best decision for yourself, k?)...
Find a can of LPS-3 it's a bit spendy, the LPS-1 and LPS-2 are common and inexpensive; but LPS-3 will keep unfinished steel from rusting when stored outdoors for 3 years.
It sprays on as a sort of foam and dries to a waxy finish. It's messy to apply but once it dries it's only a bit sticky to touch.
Take the gunstock(s) off, give the metal a spray, including inside the bore, wait a few minutes and reassemble, then leave it to air dry someplace warm for a day-or-3, put it in a gunsock and as long as you keep it someplace dry, your gun will be fine for decades (or longer).
And when it comes time to bring it back into action, the LPS-3 is easily removed with LPS-1, WD40, Varsol or the like.
For the cleaning, in your case I'd recommend Ed's Red or Hoppe's #9 (regular, not the 'Benchrest'). Both of these because they are perto-based and have anti-corrosion properties all on their own. And come as close to a "One-solution-fits-all" sort of thing. Which is probably a good thing. Currently my guncleaner shelf has 9 different bottles/cans of "stuff" on it, so one can go a little crazy with this, if you aren't careful.
"Those who have long enjoyed privileges as we enjoy, forget, in time, that men have died to win them."
Franklin D. Roosvelt