Sorry, vegetables are a little out of our line. The Lady Bird Johnson Wildflower Center, home of Mr. Smarty Plants, is committed to the growth, protection and propagation of plants native not only to North America but to the area in which they are being grown. Vegetables have been hybridized and imported from other countries so much that there is really no way that they could be considered native. Generally, the best place to go for information on growing fruits and vegetables is to the local County Extension Office, usually connected to an agriculture university in your state. In Texas, this is Texas A&M. Here are links to several websites which we believe have the information you are looking for.
Texas A&M AgriLIFE Extension Vegetable Variety Selection
Travis County Extension Office Recommended Planting Schedule (okay, we know you are in Burnet County, but it's right next door to Travis County)
Aggie Agriculture Vegetable Gardens