I live in Dallas. Stefanie, you can build a storm shelter in your back yard with no trouble if your that concerned.
But a real function basement just will not work in Texas.
They have pre casted or storm shelter that all is needed is a back hoe and dig the hole and insert the thing in the ground and cover it up. This works.
Make sure with our heavy rains that the entrance is well above the ground as to keep surface water out.
Basements are usually found in soils and states with a good rock or bedrock soil foundation. This usually takes us north to Arkansas and Missouri. Our shifting clay and other ingredients just shift so much.
When we go without rain for over 2 to 3 months which happens regularly in the summer and then we have a gully washer, our home will easily shift up 2 inches or more almost over night. When this happens, where does the basement go?
Stefanie, I would strongly suggest that you build a safe room in the center of your existing home. They have kits and plans for such projects and you get a whopping insurance discount also, especially if your in the "tornado alley". These rooms can be a closet re designed or just a small 4x4 room. You really are protecting your self and loved ones from flying missle objects. Especially 2x4's acting as spears.
Check out this avenue. You would be much happier and save money also.
Good luck, if I lived in Houston as I did for 20 years, I would worry more about the mosquitoes. LOL.
I remember hunting snow geese in the rice fields in Katy, Texas back in the 60's.