Welcome to Texas. There really is minimal land in the state that is "public" Just about all is owned by somebody including the state. You wil find restrictions on shooting in "public" lands. Hunting is the same. Pretty much own land or do a hunting lease. Cities and towns can regulate within city limits as can counties. Generally no matter where 50 acres you can do anything. I live a couple miles south of a small town, very rural, cornfield in front, hay field on two sides, on an acre. BUT, I am in city limits. Have been know to occasionally test a firearm with a shot or two in the ground. They dove hunt across the street from me! Often hear people nearby target practicing.
We do have lots of shooting ranges, including around SA. I lived there many years ago.
Best advice, find and make friends with like minded folks that have land.