There are a few roads to get across America. The two most interesting are I-10 and I-40 (Interstate highways). Interstate 40 follows much of the old Route 66 in the western states, and you can still drive along the old highway because it was the main street in many towns, large and small.
Further east, I-40 passes through Memphis and Nashiville, good places to visit if you like Elvis or American country music. I-40 ends in Wilmngton, North Carolina, near I-95, which is the main east coast highway, and can take you to Miami or New York City. I-40 starts in Barstow, California. As you leave Barstow you will see a sign which says "Wilmingtom, NC, 2554 miles", which matches a sign in Wilmington, which says "Barstow, CA, 2554 miles". Years ago I wrote my name on the back side of both signs, I wonder if it is still there.
I-10 runs from Los Angeles to Jacksonville Florida. It is quite a bit longer than the I-40 route, but runs through Phoenix, El Paso, San Antonio, and New Orleans. You can listen to Cajun music on KBON radio, FM 101 for most of your drive across Louisiana.
Driving is not so difficult on the interstate highways. There are no tolls, traffic is light outside the cities, and they are quite wide and smooth. Be careful not to fall asleep, there is a least one place where there is more than 100 miles between service stations. Rest areas or picnic areas are usually found every 50 miles or so.
If you feel sleepy, start eating something chewy, like beef jerky, or hard biscuits, this works better than loud music or coffee. Once I drove from Phoenix to Tampa without sleeping. Not wise, but I was hauling animals to the state fair, and they had to get there asap. Eating does keep you awake when behind the wheel. On I-10, it is nealy 900 miles from one side of Texas to the other, and there isn't much scenery to keep you awake.