If you have children unpacking boxes from underneath beds in their aunt/uncle's house, it doesn't sound like you need locked firearms. It sounds like these children need discipline and supervision.
Op didn't mention cost, but being a college student, I will make the assumption the low/lowest cost options are preferred.
A firearm stored separately from ammo is effectively disabled. The drawback to this is you absolutely cannot miss a single round. *IF* you can be certain to get every round, this is an effective method.
Mechanically disabled or locked firearms is a more foolproof method. Firing pins come out, for free. Many guns come with some sort of trigger lock, or a cable you can put through the action and lock. This is free if the gun came with it, or cheap if you have to get a lock or two.
If you still have the cases or boxes they came it, I'd put them back in those, thoroughly oiled, ammo separate, and mechanically disabled or locked. That's how they come from the factory, and they come out of the box rust free after sometimes months to a year on the shelf. Environmental humidity is really only a concern if there are rapid temperature changes sufficient to produce condensation. Humidity in the air only causes rusting if it can condense.
