Haha. Really, reading that you're paying for a storage unit makes my hands twitch and it's an effort to keep my blood pressure from going up. Thanks for providing followup information.
Sounds like you've got an outdoor unit, which you've put a moisture barrier in (good) and a mouse trap. Since you've determined it's definitely necessary to store these items, the best thing I can tell you now is that you or your wife needs to stop by and check the unit one to two times per month.
Checking the unit includes completely opening it, going inside, and moving things around. It's important to move stuff and not just make a quick glance over. If you get rats or mice (one trap won't help if you get an infestation) they aren't going to be sitting there nice and polite and in your face waiting for you to see them. They'll dig into the bottom of some box, of course the side that's facing the corner, and build up and you'd never know until you moved the box. The same is true for moisture, or something leaking in from an adjacent unit. You just won't have a chance of seeing it without a good investigation.
One other thing, when you go by, take a look around the dumpsters on the property. If you see a bunch of bulk trash there - that's an indicator. No one is driving their things to the storage facility and then deciding to throw them away there. When you see bulk trash like that, know that it is from people who are giving up their units but deciding all, or most, is trash, so they dump it. This will let you know if the facility has a lot of problems with their units or not.
Also, it was good to read about your Cherokee. I've got much more respect for a person driving an older car cash paid, than someone driving something new or flashy that's got a huge loan against it (except in certain circumstances, like they have the $ to back it up but got 0%).