Birmingham door to door is a reliable shuttle service from Birmingham airport to Tuscaloosa. Here’s a link https://www.birminghamdoortodoor.com/
I shipped most of my son’s dorm supplies via Walmart and Amazon at the beginning of the Fall Semester. Walmart will ship orders of $50 or more free and we had Amazon Prime which offers free 2 day shipping. Students also have access to a shuttle that runs to University Mall each Sunday http://crimsonride.ua.edu/shopping_route/ so you could shop for additional items once you arrive. There is also a shuttle to Target during Week of Welcome I believe.