Does your local bike coalition have an urban cycling class? I found this helped to learn how to handle road situations.

It looks like you have a similar riding style to me: practical rider, regular clothes, stylish bike.

Your bikes will work well but will be a little slower than a road bike. I started with a Public bike (step-through frame) but later found the geometry of that one I had didn't suit my hills well. I got a new bike a few months ago that is a slightly sportier ride but configured for the city (soma mixte).

Chicago-land is flatter so most gearing and geometry should work fine for riding around town.

The Public Mixtes are great. The "C" ones are slow. Also look at Brooklyn Bikes, for similar stylish practical bikes. And Detroit Bikes.