Congrats, I am sure you will love commuting by bike.
A lot of what you might want will vary on the types of roads you are on, amount of traffic, climate, etc. Some thoughts from my experience as a new commuter last year:
1. Get lights to SEE, even if using to be seen. Lights are not a bad idea in the daytime, and anything to dim will not bee seen. A bright tail light can help motorist see you in the day. A reasonably bright headlight is a good idea too, nothing less then 200 lumens. A lot depends on your budget - how much do you want to spend? Also how long do you need the charge to last? You have a short commute, so maybe not an issue for you. I also happen to like having both bike mounted lights AND a helmet light - I use light and motion VIS 360+ and would be happy to share what I like about it and the combo.
2. How much stuff do you have to carry? Backpacks are OK for lighter loads, but if your load is heavy or it is hot you might appreciate the option of a rack and panniers. Also useful for running errands.
3. Dealing with flats - Flat tires happen. Get some good flat resistant tires and you might go a very long time without, but nothing is flat proof. Consider a spare tube, tire levers, and a mini frame pump or CO2. Make sure to learn how to change a flat tire. If you have a good option if you get a flat mid commute, like a bus or call a cab, maybe you can just deal with it later, but I like to be prepared
4. Fenders - help keep you and your bike clean when the ground is wet. I find even if its not raining, standing water from a rain, hose, etc can still get me and my bike dirty. Keeping your chain clean seems better then cleaning it all the time.
5. Clothing for weather - don't know what your climate is like or if you plan to ride in the rain, but some good waterproof, breathable bike gear is always nice. I also love a nice vest for windy/cool days.