What type of insulation should I use for a new home In Tennessee? Should I use 2x6s for the walls?
The decision of what type of insulation to use should be based on several factors, but I recommend you consider high energy performance and local climate conditions as prime factors. Spray-on foams are more expensive, but they have a greater R-value per inch than the more conventional types of insulation.
If a thicker wall system does not present any aesthetic issues, I recommend a 2x6 wall cavity to allow for a greater amount of insulation. If you employ advanced framing techniques with studs on 24" centers, you may be able to achieve the thicker (2x6) wall cavity without increasing the total board feet of lumber beyond what you would use in conventional framing with 2x4s. Another strategy to achieve a tight building envelope that will help manage costs would be to spray 1" of closed-cell foam in the stud cavity against the sheathing and the studs themselves. You can then finish off the insulation with blown-in fiberglass or Blow-in-Blanket application. In this scenario, you get the sealing power of foam without the increase in cost. In my experience in our shared climate zone, this hybrid will provide the best return on your investment.
Joseph Lstiburek, an engineer with BuildingScience.com, has written a book called Builder's Guide to Mixed Climates that would be just right for your climate zone in Tennessee. I recommend you review it with your architect.