Greetings Mike:
Thanks for your most excellent and forward-thinking question as I applaud all parents who have the foresight to instill a strong forest conservation ethic within their family – forestry is a greatly underappreciated science and profession now of days.
The four most common nut crops grown here in the eastern US are walnut (native black walnut and the non-native English walnut), pecan (numerous cultivars), Chinese chestnut, and hazelnut. In order to provide you appropriate guidance and expertise, may I recommend that you contact an Extension Forestry specialist at Clemson University, as these kinds of questions absolutely require local expertise!
Clemson Cooperative Extension: http://www.clemson.edu/extension/natural_resources/people/index.html
Best of luck!