In Texas, by far the meat of choice is beef. The beef of choice is the brisket. The brisket comes from the breast of a bovine, between the front legs. It's boneless and usually very fatty. But if your heart can stand it, the fat imparts a delicious flavor.
Adult goats are also very popular.
It's all delicious. You will also find a lot of sausage at Texas barbecues. When you go East of the Mississippi or North of Oklahoma, pork is the barbecue. A barbecued whole hog is a delight to behold and even more delightful to consume. The folks in Kentucky lean toward mutton as the barbecue of choice.