Getting to WV from SE TX is not easy. There's so much to see between those two great places, including beautiful mountains and great cities.
Your best bet would to drive I-10 over to Mississippi and take I-59 through Hattiesburg and Birmingham to Chattanooga.
You'll switch to I-75 North in Chattanooga. I prefer getting off at Cleveland (20 miles north) and going east on U.S. 64/74 alongside the Ocoee River (whitewater) through Murphy, NC and east to Asheville, NC.
By all means, take in the Biltmore, the largest home in the U.S. It's an absolutely great foodie town, and the Blue Ridge Parkway runs right through town.
You could go north on the Blue Ridge Parkway until you get tired of the curves and slow speed limits. Then drop off on one of the side roads that'll take you toward West Virginia.
On your return trip, you could drop by Kentucky and Nashville. I suggest you just come through Bristol, VA/TN if it's handy coming back from where you'll be in West Virginia. Gatlinburg/Pigeon Forge is a great place to stop and do some hiking and see water falls. Gatlinburg has very inexpensive accommodations and Great Smoky Mountain National Park. It's all I-40 into the fabulous Nashville, my hometown. I'll stop there.