Elaine. There is a Texas Gardening Forum moderated by
@Bubbles whose name is Sandi and who happens to live in Austin. Using her avatar name will clue her in to your post here. Texas is big, but I think there are several members close to Taylor. I'm well north of you now, but I lived in Austin for a long time. I think in Taylor you will find good soil to work with. It's different from the hill country west of Austin, more farming and less ranching land there. I think the most likely lawn grass will be St. Augustine. It's widely grown and does especially well in mild winter locations.
Happy 4th to you. I hope someone brings around some Elgin sausage to help you celebrate!