Bike: get a good quality but cheap bike. Your bike should be nice enough to ride but not nice enough to be stolen. I use a Kona city bike which is a light weight commuter. The components are what make it cheap, so it has plastic pedals and the cheapest brakes and de-railers you can get. My plan is to upgrade these parts as they break.
Backpack: join the cool kids and get a backpack. In it I have a spare tire, patch kit and basic bike tools. Plus I haul my clothes, makeup, shoes and lunch for the day in it.
Backpack Raincover: This will make your backpack even cooler but you'll love it on the rainy days.
Helmet: Wear it! You will likely bike on roads and cars are not careful around cyclists.
Pump, spare tire, patch kit: City streets are full of glass and junk that can destroy your tires so be prepared to get a flat. I also recommend taking a basic bike maintenance course.
Bike commuting is quite easy to get into so there really isn't any excuse not to (well unless you live in the boonies). If you do live close enough, I highly recommend you try it out!