There is very little public hunting land in Texas.
Most hunters lease land from farmers and ranchers.
Unless you pay a lot more, you'll be sharing the property with people you don't know carrying high powered rifles. Gosh, hunting in Texas is a challenge and adventure even before you buy ammo. The time to start looking for a lease is July. Start in your local newspapers. Call the listings in your price range, arrange to meet them on the property and take a look around.