In my opinion the best insulation is expanding foam, like Icynene. Unlike batt insulation, it seals the walls and is not affected by humidity. It's more expensive than batt or blown-in insulation. A local foam contractor can look your house and give you a cost estimate. Hope this helps. Ask the foam contractor about both open and closed cell foam.

I live in South Carolina and second Ignacio's comment. We have Icynene and receive monthly updates from Duke Power showing our energy usage is lower than an "energy efficient" home.
We also have a Mitsubishi mini-split HVAC system. We built our home ourselves and I'd never go back to batt or blown in insulation.