Glad to hear so many grad students are biking! I've been biking an average of 3-5 days a week for an average of 5 miles each way. To not repeat whats been said, I know milk crates are GREAT when it comes to making the bike ride more comfortable, but if you are like me I'd rather just take a backpack. For less then 4 miles total a day, I'd suggest a backpack. Ditto on the messenger bag, its a PIA and super uncomfortable.
My suggestions:
If you don't need to be too dressy, where some comfortable jeans. Bringing a change of shirt, small towel and deodorant has done wonders for me.
Invest in a GOOD u-lock that is small. http://www.jensonusa.com/Locks/Kryptonite-Krypto-Series-2-Mini-U-L-OCK I can almost guarantee that a cable lock will lead to a stolen bike.
If you have the luxury, keeping work supplies like books at school is great. I work in a lab that allows me to keep most of what I need there. I bring lunch meat, bread, some coffee and leave it there. I also keep most of my books there. I avoid carrying my laptop as much as possible but that's usually the only big thing I carry.
Buy a bicycle travel bag. This is great for carrying essentials for efficient commuting via biking: a multi-tool, small pump and a spare tube. I've been saved over a dozen times by my pump and spare tube (everyone in Tallahassee seems to love throwing glass bottles on the road). BTW, avoid glass like the plague.
Travel bag http://www.jensonusa.com/Bags/Topeak-Aero-Wedge-Strap-Mount-Pack
multi-tool http://www.jensonusa.com/!5S3fFg4vVTEmf-qC-f!ygA!/Park-Tool-IB-3C?utm_source=FRGL&utm_medium=organic
(I own the one above and its amazing. It comes with a tire lever which makes my life surrounded by glass much better)
Pump http://www.jensonusa.com/Frame-Pumps/Topeak-2000-Road-Morph-Pump
(I own that pump also and its well worth double the price it comes at. It has a foot peg and comfortable handle plus it can inflate both schrader and presta valves. I can get up to about 80psi pretty easily)
Overall, for less than $150 you can make your bike a model of efficiency. All you would need to additionally carry via backpack is a change of clothes (maybe). I'd say its a great investment considering you'd save the $480 in parking, the gas money and get in better shape.
