I don't believe there is RV camping at the state park, only the national park. Also, you will not find a lot of roads to do 4-wheeling; most are paved and I don't think you'll need to rent a Jeep for this trip. Depending what time of year you're going, if it's hot..and it's getting there now...don't go off-roading by yourself in Big Bend. If you break down you probably won't get cell service. Take LOTS of water and let a ranger know where you're going. It's wild country out there. :)
Here's the park's web site for lots of good information on things to do, roads, camping:
Big Bend Nat'l ParkHere's the state park's site:
Big Bend Ranch State Park