Best way to insulate between studs with rigid foam
I have this shed outside that I want to insulate so I can work in there in the winter and so it will hopefully be less damp in the summer.
It's an old construction. Most of the studs are 2x3 and in some places I only have 2 inches to work with. Since I don't have a lot of depth for insulation (and I don't to start changing the structure) I was looking for the most efficient insulator. Polyurethane was my first choice but couldn't find it in rigid foam sheets so polyisocyanurate it is. (R-6.5 per inch)
Now I was wondering how to install the thing properly. First time with foam insulation so I have a few questions.
First, I need to install the stuff between the studs. I didn't find much info on the web for that. Only that (of course) it will need be tight between the studs. What's the best way to do it? Try to fit it as tight as possible between the studs? (also considering that the studs are old and not perfectly square)
Or I was thinking that I could also cut the foam 1/2" smaller all around and fill that space with spray foam? What do you think? Too much trouble of worth it?
2) Do I need to glue the foam to the wood structure of the tight fit will be enough? If I need to glue it, I assume the best thing for the job is that foam glue they sell?
3) Do I need to tape the joint between the stud and the foam with a tape like tyvek or that foil tape?
4) Would I gain a lot from using those rabbeted foam products that cover the studs with some insulation material or just filling the space between the studs would be fine?
5) Anything else I should do or I'm ready to drywall? The foam acts as a vapor barrier as I understand. So I'm all set or there are some things I could do to improve the insulation efficiency?
6) The roof. It has beautiful horizontal 10" long beams. I was planning to put 4" foam in there (R-26). I assume I should simply glue it to the roof. But how do I put the drywall over it? Driving screws in there would reduce the insulation efficiency. Glue it to the foam? A way to fasten it to the beams on the sides? Or (and even better) could I simply paint the foam with some sort of appropriate paint that would adhere well to the foam and look fine. (it is a shed after all)
Hope you can help,