For your situation, I am going to suggest that you consider evergreen shrubs which will provide the screening you desire more quickly than most trees.
Mr. Smarty Plants has received numerous questions about plants for privacy screening over the years, and this one from Buda seems tailor made for you.
This answer for a question from Magnolia, TX has plant suggestions and also explains how to use our Native Plants Database which will help you select other plants.
This answer for an Austin question may also prove helpful.
The folks at the Hays County Office of Texas AgriLife Extension could be another source of help.