I can vouch for banana boxes since they're sturdy. But they have a lot of small openings in them so use them for medium to big items like clothes, books, DVDs or you need to line them.
I like to make different projects out of cardboard. But what I have noticed is that neither hot-glue or duct tape are really good solutions here. The best bet is to use a box tape specifically designed for sealing cardboard boxes. The glue they use is activated by water, and slightly soaks into the paper surface of the cardboard. The seal is very strong, and the paper tape itself becomes just another layer of the cardboard at that point. You're essentially turning two pieces of cardboard into one larger piece by lamination.
The other advantage is that doing it this way gives you a paintable surface that's very similar (identical, really) to the rest of the cardboard, so your paint will be seamless.
A good package store like Staples should have the water-activated box tape.
Once cured, I believe that the box tapes are pretty resistant to humidity, but I understand your point. The problem with "clear box tape," in my opinion, is that the adhesive comes off easier. With the water-activated paper tapes, once the adhesive dries, you end up tearing the cardboard apart to get the tape off.
An experiment might be warranted - do one of each and see which works better for the intended use.
For my kids we will also use newspaper strips in watered-down Elmer's glue mix works great. I was suggesting either paper mache or clear packing tape. I've done a lot of cardboard costumes and have used both. The nice thing about paper mache is it's easily painted and you could use wire or staples first and then cover it with paper mache for probably the BEST assembly.