I'm a grad student--I hope to start my last year of university very soon.
I ride about 20 miles roundtrip in the summer (the shortest route would be 12). I don't have the patience to stay below the sweat threshold (for me that would be around 12-13 mph), so I wear lycra shorts and a jersey and change at work.
Fenders, decent lights, and pump/patch kit/spare tube are essentials. I also like to have the tools I need for cable and brake adjustments (just a couple of allen keys for my bike). Just about anything else is optional--you'll soon figure out what you need and what you don't.
As a final note, campuses are high-theft areas so make sure you know how to lock your bike securely, and don't commute on anything you can't afford to replace.