Hi K. Caudle, I think your problem may more of a moisture control question than anything. I recently moved a house and had to address this issue. Given you will have central air in a warm climate you will need a vapor barrier on the outside of your insulation. Without one you may accumulate moisture in the insulation and rot the stuctural members of your house. Since you are opening up the exterior walls from the inside, icynene insulating foam might be your best option. It's a vapor barrier as well as an insulator. Unfortunatly, it's rather expensive.
Another possibility might be to place a vapor barrier in the open walls and cover the exposed studs with the barrier but push it back into the cavities and then place something like batt insulation in the cavities. I would, however, get a second opinion on this idea.
As far as "economical" is concered.......batt insulation can be a do-it-yourself project where icynene is not.