I am moving in a few months from West Texas to Virginia. I am not familiar with how expensive shipping my car would be.Would it be better for me to just take the roadtrip?

Why don't you explore your options by getting quotes on shipping your car; then determine how much gas you may consume making it a roadtrip. There are other factors in the roadtrip as well, such as stopping for meals and sleeping.
Tick

The biggest is dasautoshippers.com. Not the cheapest, but considered the best.
Just put in the 2 zip codes and get an estimate. Probably in the $1200 range. The drawback is they don't deliver door to door.

There are companies that hire people who need a one way ride to drive your car to its destination. This may be a less expensive option then shipping it. My brother used to do this to get back to college each year.