If you're talking Washington state, I highly recommend Hog Haulers in Portland Oregon. Good equipment and really good people. I don't know whether they cover Texas but I know they have at least 1 truck that goes east-west.
Whoever you use, just make sure you are dealing with the shipping company and not a broker. With a broker, it may be a little cheaper but your car can be moved in stages by different transporters with changes in trucks and iffy schedules. Most of the online quotes you can get are actually brokers.
Also, be sure you are getting an enclosed transporter. Open is cheaper but riskier.
I used Hog Haulers to bring a BN1 from Oregon to Arizona, VIP (southern Calif) to send a car to New Jersey, and Roads Scholars (from somewhere in the Northeast) to ship a car to New York. All were good experiences at my end.
Marv James