As usual, LBE knows her stuff, but I've got to disagree on several things. The sort of commuting you are looking to do is totally different than the sort of commuting that she does. Until you know that you like it, and that you are going to stick with it, don't invest in all that stuff: buy the floor pump, the lights, the helmet, the D-lock and chain, and that's it. Wear a backpack instead of investing in panniers, drive on rainy days instead of buying and installing fenders.
If you are still into it at the end of the summer, go all out to make your ride more comfortable and efficient. I cycle absolutely everywhere -- to the shop, grocers, bars, parties, work, movies et cetera -- and I ride a steel 1980's Raleigh 10-speed with suicide brakes and stem friction shifters, carry an old canvas messenger bag, and wear my D-lock and chain like a bandoleer. I love it.