The three Texas regiments were recruited with the intention of serving in the East, so it's true that it consisted of some of Texas's first and most determined recruits, who wanted to fight where it was believed the major, decisive battles would be fought. They were mostly younger men who had been born out of state (though most people living in Texas were at the time), coming from middle class families. In comparison to many of the Texans who enlisted later and in units that would serve in Texas or in the Trans-Mississippi, they tended to be more loyal the South and the Confederacy, and more enthusiastic about secession. While they did consider Texas home, some who had been born east of the Mississippi also wished to fight for their former hometowns and states of birth as well.
I definitely second Ural's book mentioned above. It covers the social and demographic aspects of the brigade it great detail.