When you are ready, buy from a reputable bike shop. If a bike is not assembled, tested, and adjusted by professionals, you are courting disaster. A helmet leads every list of essential accessories. You should never even ride across a parking lot without a helmet. Cycling in the Texas sun makes a helmet with a fitted visor a welcome addition.
All states require a white front headlight for night riding.
Mounting reflective material on your pedals, wheels, and seat post will make you more visible. The next accessory or accessories you buy concern the bicycle seat. A touring-style sheepskin cover is worth consideration. Cycling shorts add comfort, too, if you buy them correctly. When buying shorts, make certain no seams run down the middle of the crotch.