I wouldn't worry too much, I have used shotgun ammo 40 years old! I found the shot becomes a bit oxide coated and the powder sets into a block which crumbles. Any corrosion can be wiped off the brass head, but they still work OK though some of the old nitro loads pack a fair punch at either end !!
You could get an ammo box from surplus Army sources (50cal or 7.62mm cal is fine) and they are relatively air-tight. For a better job a tub with a needle valve from the same source is better with a clamp-down clipped lid, used for 1"AT minigun rounds, I believe.
Silica gel - I have used for small areas in photography in tropical conditions for lenses etc, but a candle stub uses up the air as well and is cheaper than gel, though a small amount of water-vapour would be added by the combustion I suppose.
Simply storing in strong,air-tight, black plastic with a hot-wire seal works well too, -not unlike a freezer-bag concept.
Unless it is 'special purposes'(wink-wink)ammo, I like to turn it over by using the oldest first.
Have fun, everyone should have a bit of extra ammo somewhere, just dont forget where you put it [like I did a while back when it was needed urgently].