It will be a long, hot, flat ride from Houston until you get out of Texas. The two-lane highways offer a little better scenery than the freeways, though.
As far as tents, if you don't mind small and light, I'd check out REI.com for some of their backpacking tents. They may be on the pricey side, but they are all good tents -- small, light, and will keep you dry in the rain. I'd also recommend getting some kind of light backpacking tarp and some nylon twine. You can hang the tarp from trees and have a place to hang out that is protected from the sun or the rain. Also a good place to keep your gear overnight if you go with a 1-person tent. Or, even set up your tent under the tarp for a little extra protection from rain.
There are two REI stores in Houston, so you can stop in and see if there's any other backpacking gear that you *need* for the journey. Stove, camel-bak, water filtration?
Instead of heading west on I-40, you might want to consider heading a little further north into southern Colorado and Utah. You could ride through Pagosa Springs and Durango, CO, head over and hit the 4 Corners area, Monument Valley, etc. And, if you have time, you're not going to be too far away from some of the US's real treasures -- Natural Bridges National Monument, Bryce Canyon National Park, Zion NP, North Rim of the Grand Canyon. All would be awesome rides and are well worth an extra few days. All of the National Parks have campsites, but you may need to book sooner rather than later to get a spot.