I recently moved into a house with a 12’x16′ barn style shed. I installed a window unit and run it a couple days a week while I’m out there. It works well enough most of the time, but I’d like to insulate the walls and roof to help out on the hotter days.

It’s just osb siding and studs, so I believe I’ll need to caulk a moisture barrier inside the stud bays toward the outside of the shed?

So… any recommendations for what sort of barrier and insolation I should use would be appreciated. And should I do something different for the roof than the walls? I’m leaning towards rock wool over fiberglass. I considered froth paks, but that seems expensive and more of an ordeal.