Drive to Lubbock. Spend the night. Drive to Corpus. It's easy. Lubbock is right at the half-way point.
When I travel (and I recently drove across 7 states, from Hampton, VA to Denver, CO--hey, neighbor!), I start with a trip to my mechanic. I tell him I'm planning a long trip, so could he check everything? I make sure I know how to change a tire and all my fluids myself.
I pack a small emergency kit, with a flashlight, a first aid kit, fluids for my truck, some rope, a knife and one of those thingies that can cut a seatbelt or break a window. Also a tire guage, a small tool kit and a few rags. (Since I was driving across country in December, I packed a space blanket and hand warmers, etc.)
I figure out where I'm going to stay overnight and make a reservation. I program the address into my GPS, but I bring a map in case I have to change my plans. I program my phone with numbers for the hotel and any emergency services I might need. A triple-A membership is a good idea if you break down and need a tow, but you may be able to get a similar service through your insurance or even your cell phone service.
I make sure that I have plenty of music to listen to on CD or my iPod. I buy a couple of audio books in case the music starts to get boring. I pack a cooler of snacks, because sometimes when I start to feel tired, I can eat some nuts or cheese and keep going.
I eat a good breakfast before I leave. I stop for lunch and spend some time just walking around, getting the circulation back in my butt. I arrive at my hotel in time to relax for a little while before going to dinner. I recommend Holiday Inn Express, because it serve a free breakfast every morning (go early if you want eggs).
I packed my gun because I was traveling alone. But first I checked the laws in each state by going to the state police web sites. I had to unload my gun and put it in the back of the truck when I got to Illinois. I made sure my concealed carry license was recognized in each state and bought a holster purse.
I drove across 7 states just with my GPS. I programmed in the address of all the hotels and just followed the instructions. Sometimes I didn't even know what state I was in unless I stopped and asked.
Try not to drive at night. That means not leaving before sunrise. Make sure you have water in case you break down and have to wait a while for help. Call a relative whenever you stop so someone knows where you are.