Tires depend on the quality of the roads you will be riding. Chances are, regular tires will work fine, but you might be changing flats on it if the roads are trashy, or you don't keep them inflated and you get a pinch flat. I'd ride bigger puncture-resistant tires, or at least get some Mr. Tuffy liners to put in them.

Other than that, pretty much anything will work. Stay warm, stay dry, and don't worry about speed. I'd also recommend getting a mirror of some sort, it will help a lot with traffic.

Since you're only riding it 2 days a week, I'd say go ahead and ride about the same distance on one other day each week. 3 times a week is plenty enough for your body to adjust.