We love any public park be it a state park, national park, national forest service, Corp of Engineer, county or city park. All have different camp fee so you just have to investigate each one. If you're a Senior you will get 1/2 off on camp fees in many public parks. Sometimes we'd only pay $6 or so. We didn't need hookups. We have found the Corp parks to have excellent facilities. Many state parks have big scenic sites, good roads and good facilities. Each one is different so you have to do your research.
RE: Texas State Parks:
There are a few options for a non-resident - purchase a yearly or if you qualify for age there's a senior pass. There's also a Texas resident senior pass.
http://tpwd.texas.gov/state-parks/park-information/passes/park-passes