I have mine sitting in the driveway on a set of saw horses. The inside never gets wet because of the way that the top is designed.
If you cover the top with a sheet of plastic, it will "sweat" and cause moisture and mildew problems. Mold will grow. It needs to breathe.
Just keep it off the ground so it doesn't draw ground moisture and don't worry about covering it. Give it a good scrubbing inside and out before you install it.
'87 YJ, 4.2L built and bored, 8" of lift, 8.8 rear, AX15/NP 231J, Tom Woods drive shafts, Flat fenders, 12,000LB winch, Custom bumpers, Rattle can paint job. Never completed...