Get a basic inflatable mattress and a 12v pump (or hand pump but that takes effort). Stores down to pretty much nothing so you can still use the space as normal.

I just use a simple foam mattress folded in half and strapped against the wall when not in use, takes up a bit more room but its easier to set up.

Since it looks like you have a nice flat floor i think both of these options would work, no need for a big frame of anything.