Closed-cell spray foam, about 1" should do what you need it to do. It's flammable, so you would want to sheath the walls with drywall or metal.
It acts as a vapor barrier, so if you ever wanted to increase your R-value you can go with regular fiberglass batt right over it.
A vented heater would be a good investment, too.
We used foam in the house we built a couple years ago and have been very happy with the results.