If this Murphy Bed is used for guests, I suggest one of these Two Sided mattresses.
The thinnest is the Tulah in firm.
Old Fashioned made Two Sided Mattress that you can flip. Strong coil unit and NO Memory Foam. Durable for Plus Sized People. Works with Adjustable Bed Bases.
If it's you, who will be sleeping on it, then I suggest one of these all natural latex mattresses.