As BobSc and PaPow said...
It depends on conditions. If you can't keep the room where the safe is at a reasonably low humidity, and you can't relocate it to a drier location, nothing is going to work well enough to count on without constant attention. If that's the case, consider a second line of defense, or even a third.
A good film of oil or other corrosion-inhibiting oil or wax is your first defense. Good practice anyway before putting something in the safe is to wipe it down and get any fingerprints off before the acid and salt in those start attacking.
Vapor Phase Corrosion Inhibitors (VPCI) disks and blocks (like RustBlox) are available from most gunsmithing supply houses, and I generally keep a few in the safe, just in case. There are also toolbox drawer liners with the same stuff in them. Those won't help with wood stock stability, so far as I know, but they'll protect the metal.
Third line of defense would be plastic bags or some other airtight container. Brownell's sells what they call TRIPLE TOUGH™ PREMIUM STORAGE BAGs, which have a metal foil coating, are puncture resistant and are supposed to have 0% moisture transmission, even in contact with earth. Another option would be a Foodsaver. Those have the advantage that you can cut the bags (tubes, actually) to any length, heat-seal the ends and suck the air and any moisture out before sealing. For something you take to the range every month or so, that's actually a decent option. Just cut the bag a few inches too long. Then, when you want it out, just clip off the end, and when you come home you can seal it again. The vacuum sealing also shows very quickly if you've got a hole or a bad seal in the bag, too. That's after wiping it down and oiling, just as you would before any storage, and there's also no reason you can't put a VPCI disk in with it, too.