^This is excellent advice.

Things you need: the right size bike!!!, lights, fenders, good slick (not knobby!) tires, low gearing (to make the hill easier on the way home). Allow me to recommend Kool-Stop brake pads. I think helmets are good.

Things you probably don't need: Racks/panniers, suspension, disc brakes, drop handlebars, high-end components. A lot of people like racks and disc brakes for commuting, but six miles will be fine with a backpack and the V-brakes you'll find on most mountain bikes have plenty of stopping power. Don't kick in extra money yet. Once you know what you like and don't like about your bike, you'll have a better idea of where your money should go.