Best Company to get my experience with. Houston, TX

Roehl dry van National Fleet is ok.
You can probably do better than the others on that list:
Freymiller : hires new cdl grads & drivers with less than 6 mos. experience for their "Restore Program."
FFE (Frozen Food Express)
Titan Transfer - trucks run 70 mph.
Abilene Motor Express - trucks run 72 mph.
Navajo Express - fly you to orientation in Denver,CO
MCT Transportation

 

You did graduate from a cdl school, right?

 

Good; community college programs are really helpful on a job application.
Danny Herman Trucking is dry van and most runs are south of Interstate 40 and coast to coast. Lots of Texas border towns and has a terminal as far west as Calexico,California.
Danny Herman Trucking does hire new cdl grads that have a 85 GPA from cdl school. Ignore the "experience required" on the website.
You can make a good living and get good experience with any of those I listed though.

 

@Lancross hey brother also don't forget to check service transport as its tanker and you can make pretty good money with them, one thing I know for sure is you pick up a load and come back to Houston. Instead of hurry up and wait deal.

 

Prime seems to be a good company as well.

 

Also if you want there's local job city P&D avaliable especially now since it's peak season.

Here are the list of companies who will hire you like Mr chinatown says ignore the requirement experience just apply.

Southeastern freight
Saia freight
Averitt express
Southwestern freight
Ceva logistics
Old dominion
Aaa Cooper
Yellow
Vocar
US food
McLane
Sysco and sygma.
There's few more I can't really think of it but ltl companies are really looking especially after the truck show they had at nrg few of the companies I wrote were really looking for drivers.

Good luck and be safe.