1965 Overlander is a good choice.
I am a Vintage snob, focused on the Pre-'69 late sixties five segment end-cap trailers. This era is a great candidate for a “Keeper”. With a handyman's pallet of tools, you can build a way better than new trailer. I'd say that they're the easiest to rebuild. If I were to build another, it'd be a '68 Trade Wind.
Since few will notice the year-to-year difference…
My first restoration/preservation quality bath suggestion for your trailer without a bath would be the '67/'68 “Penthouse” (Airstream's official nomenclature). It's a half-dozen pieces of plastic. You'll need a '67/'68 Black tank, some new rear sub-floor, there's room in forward bays for a small grey tank with a 2” drain that can squeeze by the black tank and join with the dump valve, to drain from street-side within bumper box exactly like original layout. Water heater may require relocation.
After that, I'm looking at the '65-'68
Caravel wet-bath. It's a good size, and also found in the '65/'66 Globe Trotter.
Lastly, I'd scratch build a custom, ultralight bath. A fun project too.
Bathrooms are a lot of work. If Keeping the trailer, I would probably not consider the '64-'66 “Airline” bath and black tank configuration, although it would be the easiest, quickest, cheapest path to useable, especially if the black-tank remains functional, and secured in place. Then I'd sell it and find a dry '68 Overlander or Trade Wind to improve upon..
Finding the plastic bath will be a game of patience. An ad in Airforum Classifieds should work.
Dig in...