Since you already have the shed, you can make it work without to much effort. First I wouldn't cut the door I would cut a hole in one of the sides to use as a door. Using 4x8 ft foil faced foam insulation put a lower ceiling in at a height comfortable for you. Insulate the walls and floor with the same material. Tape all joints with an aluminum type of tape. this is as good or better than caulking to stop drafts Put plywood on the floor over the insulation and then up the sides at least 12 inches to protect the insulation. When doing the ceiling I would use 2 pieces of insulation with a thin piece of plywood in between so you will have something for screws grab onto when hanging you light fixtures etc. This insulation is very light in weight so a couple 2x3s or 2x4s from side to side will support your new ceiling without problem.