...I wouldn't have insulation board between the floor and wall, if that's what you're thinking.
You can solid insulate the exterior of the foundation walls up to grade, insulate under the floor, then insulate the interior of the walls over grade. I don't see any reason you can't insulate the interior with solid from the wall to the floor except you'll have to build out the walls or have a shelf. You're electrician might not like it much.
2x6 for sure, and you could go 2' O.C. to save $$$.
I'd use Green Zip for the wall sheathing and Red Zip for the roof sheathing and tape the walls real good, I only tape the roof if I'm not shingling right away. I wouldn't use OSB on a dog house.
You haven't said what your plan is for the roof system, but I assume you're drywalling & insulating the ceiling.
If cost is not a concern and you want the best there is, closed cell spray insulation is the way to go. It will cost a lot more, but will save in heat and A/C for the life of the building. Plus it adds stability and sound proofing to the building.
Adding up the cost of fiberglass and solid on all the walls, spray might not be that out of line cost wise.