I'd echo everyone else about buying used and taking your time with major purchases. A mattress should be new so as to avoid any chance of bugs, but otherwise, go for used, thrift, etc.
I took a peek at your other thread and saw that you'd be taking a car. I'd suggest packing up a box of basics before you go. Your mother or some friends may have unwanted things if you don't. Think in terms of things you'd need for camping in an empty apartment for the first weekend: silverware for one, a coffee mug, a plate, a bowl, a kitchen knife or at least a steak knife, a cutting board or at least a spare sturdy plate, a travel mug that can also be used in the car, a medium saucepan, a can opener, a wooden or plastic spoon for cooking, a roll of toilet paper, a roll of kitchen towels, a bath towel, and soap. If you have space to be more elaborate, you could bring a sleeping bag or an air mattress and a set of bedding, a frying pan, a folding table, a folding chair, a sponge, dish-washing fluid, measuring cups, a bottle opener, and a French press or coffeemaker. If you bring that much, you can take as much time as you need to pick out other things when you get to Texas and get a better sense of the place you'll be living and the options that are available.