That far south of the Mason-Dixon Line, I believe it is obligatory to plant sweet potatoes, okra and black-eyed peas.
For the shady areas, two plants that thrive in an open shade environment are Pawpaw fruits, and "ramps" (wild leeks). They both do very well in the humid southern areas. Ramps are commonly grown in SC, but have had some recent publicity in the north. They are now bringing premium prices from gourmet chefs. Once established, they are perpetual...like multiplier onions.
Another crop that once was a part of every southern homestead, but is now getting rare are potato onions (Tater onions). They are technically in the shallot family, and they will store longer than any other onion...this years crop will hold over until next year's crop is ready (if you store enough)!
By the way, those pecan trees look beautiful!
EDITED to add:
You owe it to yourself to check out this link:
http://www.state.sc.us/forest/nur.htm