You mentioned it in passing but I'd really suggest finding a way into a credit union. I was able to get a local credit union account shortly after graduating. Opened a savings account, a checking account, and got a preapproval letter for a car loan on the same day. It may be hard with your current part time situation, but if you go in just be able to prove reliable income to them. As it gets closer to September, this will be easier. In my case I took in a copy of my signed acceptance letter for my new job starting a week later that had the salary on it.
From the little I know in general and what I've seen around here, credit unions seem to be the go to place if there's short credit history. Easier to talk face to face too about limiting issues on your credit score rather than over the phone with a large company.