Staying at Walmarts and such

Some Walmarts/Sams Clubs allow overnight parking and some do not. All you have to do is ask, or phone ahead. Some highway rest stops allow overnight parking and some do not. Some truck stops allow overnight parking but they are usually a little noisy. Here is a website that may help you: Free Campgrounds
Since you are leaving Wyoming and going to Texas, I assume that you will be armed which should take care of any security concerns, but situational awareness of your surroundings is always the best thing to do first. If it does not feel safe, move on.