You can consider applying for the Discover it® for Students credit card. There is no annual fee or activation fee. The issuer will report your credit activity to the major credit bureaus every month. You will be able to monitor your credit progress because your FICO credit score will be included on every statement.
The Discover card also has a rewards program. You will get 1% cash back on all purchases and if you enroll in additional rotating bonus categories you will get 5% cash back on some purchases.