Spaces with still air and a temperature differential are what give you condensation. If you can either eliminate the air spaces or prevent the moisture laden vapor getting into them (vapor barrier), you can avoid it.
I'll leave it to others to comment on the wisdom of making such a small space airtight (there's a thread about it in here somewhere), but many of the build journals I've read have insulated walls.
I can tell you from my own experience that rigid foam is better than fiberglass batts and some builders here have built their trailer's structure out of foam.
I would question the 3/4" ply for two reasons.
First, is the weight issue - overkill isn't bad in itself (especially if it's free!) but I wonder if it's a false economy because the frame and suspension will need to be beefier, fuel consumption will be higher, and a bigger tow vehicle will be needed. Presumably you've already got the rig to pull it so I assume that one's a wash. If you're using the frame in your album, I could see that thing getting to its gross weight pretty quickly with heavy ply.
Second, there are a few products that can be sprayed on form ply so it breaks loose. I would be concerned about the smell and the fumes. Remember you'll be sleeping in this box for hours at a time in (hopefully) warm weather.
Then again, I'm just some guy on the internet throwing in his .02 so I could be full of it
