Welcome to the forums! Not a bad bike, but I bet you could find a bit better going to a bike co-op. You can use anything with 2 wheels for a 3 miles commute. Reading and researching is fun and all, but really you have to start riding to find out what you really like/don't like and need vs just want vs what you thought you needed is just unnecessary weight. Personally, all I think you need is a good floor pump, a frame pump, an extra tube, a patch kit, tire levers (instead of trying to repair a flatted tube on the ride, just replace and patch it later), a lock or two and decent lights. For 3 miles, you can carry all of that on your bike (mount the frame pump, the rest put into a small bag beneath the saddle), or a backpack/messenger bag. And remember to check your tire pressure every couple of days. No need to over complicate things.

A quick and dirty rundown of accessories and estimated cost

Floor pump: $40 (you can cut this in half if you get something from Wal Mart, but I like a quality floor pump)
Frame pump: $15-20 (maybe as low as $10)
Extra tube: $10
Tire levers and Patch Kit: maybe $5, but probably less
Locks: $50 (you can probably easily get away with spending less at Wal Mart, and that much on just a solid ULock )
Lights: $50 (again, you can easily spend more or less)
Optional: Helmet - $40 (I say optional, bc if my commute was only 3 miles I sure wouldn't worry about a helmet. That is up to you, though)

You don't have to spend money on things like fenders or racks and panniers at this stage. As I said, a 3 mile commute or hopping around town isn't going to make carrying a backpack or messenger bag a hassle. I also wouldn't worry too much about replacing the tires yet. It would make the ride nicer to have slicks, but if you are strapped for cash, I would focus on accumulating what I had listed out first, as not having those things can cut a ride short real quick. Also, practice changing a flat at home before you have to in real life