1.5 miles I'd use a backpack, and ride in whatever clothes I worked in. Maybe, without carrying clothes, not even a backpack. Keep a change at work, just in case.

Sure you could walk it, but I'd still ride. Depending on the overall hassle. It's not really logical to select your bike based on a really short commute in my opinion. I'd say choose one that you'll ride otherwise, recreation, sport, utility, or mountain trails or fixed gear if that's your thing, and use that bike for the commute. Any other equipment - I mean lights, pump, anything else - depends on specifics of your ride. If you don't mind walking your bike for a mile for example and have decent tires, you might find it more convenient to not carry patches and pump. For daylight commutes, lights aren't all that necessary or at most some cheap blinkies. I'd be inclined to just hop on the bike and ride it.