Welcome to the confusing and controversial world of building envelopes. To further simplify and confuse: Airtight is most important, and thermal bridging is more important than R value (to a point). Fine Homebuilding has a new Lstibureck article out on foam sheathing that is a must read for those interested in this topic. A couple takeaways: choose XPS over EPS. Strongly consider a rain screen. Upgrading to 2x6 gets you another 2" of CAVITY insulation. If youre considering foam sheathing then hopefully you know the many weaknesses of cavity insulation. I would prefer thicker foam sheathing staying with 2x4. I would also put the housewrap on the outside of the foam. Its not doing you much good between the sheathing and foam. If you get the right thickness of foam sheathing(as jlizer suggests is 1.5") then youre sheathing will generally be kept warmer than condensation temps. The real challenge of course is preventing what happens in worthy's pic. This is possible to do with tapes (ZIP system, others) and sealants but having a house wrap to integrate with flashing is a nice detail that doesnt rely on a particular chemical companies formulation. Havent done the double stud wall yet but to me it seems more trouble than its worth. It doesnt reduce thermal bridges at plates or your floor bands and eats a tremendous amount of interior floor space while reducing the amount of light (and heat for passive solar) that your windows let in. I would consider the ICFs for basement. @Robin; not everywhere else because they are expensive and dont take to changes very well. Better yet, look at pre-cast concrete walls (Superior is one brand) The complications listed above with wall thicknesses and furring for siding is one of the many reasons we have been using SIPS. Its great you are aware of the importance of air sealing. Strongly recommend you have a blower door test done at the framing stage. What you dont measure you cant improve. Here is a link that might be useful: Blower Door Test Explanation w pictures and diagrams

Nope, don't mind. We are almost 4,000 sq. ft. Three bedroom house, not large bedrooms but the single living room, single dining area, kitchen are largish spaces with the sometimes-highly-criticized high ceilings everywhere. ;~) I love 'em! We have some square footage that most folks wouldn't want or need because we have a section of the house that consists of two office spaces and a "dog room" and a largish back entry area that also functions as mud room (partly because we work at home and partly because we live with dogs and this is what works well for us.) We also have a hugely high central hallway to be an "air chimney" with high windows that can open remote....when they are open they create a natural air flow through the house windows and up and out the high windows. Obviously our house is designed for a climate that is hot most of the year! I wish I had a better engineering answer for you about why we haven't needed the makeup air, but I suspect it is simply because our house isn't as tight as hubby wanted it originally. We did a lot of research into ICFs and SIPs and tight houses, and had originally intended to design and add a makeup air infusion system. We did see some articles indicating that while it is possible to design and build a house tight enough to need makeup air, that in general "real living" some houses would not need it. In practice, we have not needed it, and that is probably because once I got through adding the fireplace (even though we chose the tightest sealed damper we could find) and the dog doors (though we can close off that room with a weather-stripped door when we want to) and we also have two vents for the whole-house exhaust fan (which are *supposed* to be sealed but probably aren't as tight as their specs)...well, basically anyplace you have a potential pentration like that probably lets more air in than you expect. Anyway, those exposures are probably why we haven't neded the make up air. We do have very strong exhaust fans (large Panasonic whisper quiet) in the bathrooms and in the utility room where the cat boxes are, and in the kitchen.....those seem able to work great with no makeup air...probably because of our "unintended" air penetration places. If I turn on the whole-house fan to exhaust, either in the main part of the house or in the "dog room" I can feel and hear the windows and doors suck in, and doors in the house that are partly closed will close....we definitely have to open some windows...so the house IS at least that tight. Does all that make sense? It's tight enough that we have a MUCH higher comfort level during cold spells (no drafts at all, floors stay very comfortable) and during very hot spells than any house we have lived in before; our utility bills are lower, our a/c is much more efficient during humid times. I think the nice tight envelope due to the ICF and SIPS and sealed attic,good windows, etc. just go a long way to making up for our other "air penetrations" caused by how I wanted my house to live (lots of windows and glass doors, dog doors, etc.)

You need to fir out the interior and create a stud wall around the entire perimeter. You also need insulation below the floor, and at the ceiling line. The stud wall will give you room to run the required electrical and attach drywall. You will also need to update your windows in any bedroom to those that permit emergency escape. You also need a plan for the rough plumbing creation, which in your location will easily freeze. Which is why many homes have basements. And all of that presumes that the building has an approved foundation type for a residence, and the local municipality will permit its reassignment from agricultural to residential. The typical pole barn foundation into dirt is not approved for a residence. A pier and beam foundation would, if the piers are concrete and below the frost line. But that causes many more issues with the needed insulation and plumbing in your location. It's unlikely that the building could be as cheaply converted to a residential classification as a new build designed to fulfill those requirements be built correctly from the beginning. Retrofitting is always much more expensive. Especially without a proper foundation.

I like extruded polystyrene foam boards attached with tapcon anchors and washers. You can use a construction adhesive with it but it's not needed. The foam has to be covered with 1/2" drywall for fire reasons. You can either apply drywall directly to foam or build a stud wall in front of foam.