Southern species which have attack-resistant heartwood include the cedars, black locust, red mulberry, osageorange, and old-growth cypress.
Old growth bald cypress was once considered a highly durable species. Research has shown that today's second growth cypress is not naturally durable.
Wood cut from several western trees, including redwood and western red cedar, is often considered to be naturally durable. However, when these species are used in the South, the durability of the wood is, at best, variable. Much of the wood cut from these species will decay or succumb to termites in just a few years.
So... use a pressure treat for the framing, order the 0.40 Retention (lbs/ft3) Ground Contact that is better for termites.
The new pressure treament requires special fastners, so get double zinc coated or stainless steel nails & hardware
Use a post base (Simpson strong tie) that has a 1" seperation from concrete to post, and coat all wood cuts with copper napthanate.
The decking if you are in termite country look into composites. Here is an article I put on my web site a few years ago, but it holds up: http://www.altereagle.com/Composite_Deck.html
I prefer Trex, with 19.5 o/c joisting, but you'll be better to decide for yourself, dependent what part of the country and side of the house you'll place the deck.
Final note, be sure to check the termites didn't migrate into the house and get the old deck removed as soon as possible.
Check my deck site for designing the joist spans, beams etc there are some charts on there we use in CA decks
Alter Eagle Construction & Design