Insulation, Radiant and Vapor Barriers - Turning a shed into a workshop

I moved into a house that has a fairly large shed built strictly for storage. It has a papered and shingled roof. The walls are a very thin 1/4 inch board of some sort (not wood), with vinyl siding. There is no paper between the board and the siding. I have already wired the shed and I now what to insulate it but I really have no idea how to do it. It will be cooled by two window A/C units. It will be heated by baseboards. The floor is just particle board on top of the frame. Most of the shed has a large gap under it as it was built on an incline.

How should I insulate? Should I use faced insulation? Should I install a plastic vapor barrier after the insulation?

Thanks.

Welcome to the forums! Depending on the type of framing and its spacing, if 2x4 use R13 Kraft insulation in the proper width. If 2x6, use R19 kraft faced. The kraft facing should be placed toward the inside of the room. Plan on covering the walls on the inside to protect the insulation. You can buy some cheap paneling to do that with if you wanted to.