Air mattress or plywood under foam mattress on sleep sofa?

Firm mattress topper or futon for me. Air mattresses tend to sag too much for me, I like a really firm bed, find many "luxury" hotel mattresses too soft just because the memory foam topper is too thick; I have to keep track of who has the right bed.

For you, it depends on what you need. Frame digging in suggests you need something firm to spread the load over the whole sofa, then mattress on top.