Texas is pretty good. For carry the Department of Public Safety (state police) issues a LTC (license to carry) and they dropped the fee to like $40 not to long ago. They are more like a drivers license in look with a photo and feel. To apply you need thevstandard personal paperwork, proficiency class certificate, be a resident of Texas for 6 months and it’s online after that. It takes about 45-60 days for a new LTC to be issued ... the DPS actually does do a real check into the application information and such. The LTC like the NC CHP can act as a substitute for the NICS check when buying from a FFL if the FFL chooses to do so. You need a LTC to carry be it concealed or open (they just started open a couple years back but you need a LTC). Pretty standard on where you can carry but Texas has regulations for No Gun signage that is more gun owner friendly, they are big and clearly written and posted up front and in plain sight ... they ain’t attractive either. Texas was one of the first states to allow concealed carry on college campuses but the individual schools may make certain zones gun free which is being argued still.
As to buying Texas doesn’t have any “purchase permit” or waiting period for hand or long guns ... basically Federal Laws and Texas Laws go hand in hand. Private sales are fine as long as both parties are Texas residents (same Intrastate vs Interstate private sales Federal regulation as any other state). FFL sales are standard Form 4473 sales with the NICS or LTC background check.
Texas is gun friendly with Castle Doctrine and Self Defense Laws also ...