If you're sufficiently concerned about the condition and preservation of your coins to go to the trouble that your describe...
1---You might want to verify that the atmosphere the coins are briefly exposed to when you encapsulate them is as free as possible of sulfurous contaminants. It'd be a shame to go to the trouble of encapsulating them (with "white glove treatment") and have a brief exposure to sulfurous contaminants set the coins on the road to possible blackening via toning while in their capsules.
2---You'd probably do well to store the encapsulated coins in military surplus steel ammo cans. Good ones with robust, viable gaskets provide excellent protection against atmospheric exposure and the only alternative that provides equivalent atmospheric protection is those high-end photographic gear cases (HPRC, Pelican, etc) but those things are really expensive. Putting encapsulating coins into a plastic bag or non air-tight box would be a half-measure after going to the trouble of encapsulating them.