First, the pack should have both a waist and a chest/sternum strap. Second, it should have enough volume to carry everything you need, with a little additional room for anything extra you might pick up during the day. Third, it helps if it is has some reflective parts for increasing visibility when running during low-light hours. Fourth, if you plan on running in all weather conditions, it should have a raincover. You can buy them separately if the pack does not have one built in.
Whatever you normally run in will work fine. You don’t need to go out and buy any special shoes for run commuting, though you may have to buy shoes more often if you become regular run commuter!
Running clothing, at the very least. A backpack if you want to carry your gear in each day.