Either a road bike or a cross bike should do, but I would think again about the flat bars. Regardless of how you feel about drop bars, they give you a lot more positions. You can still ride on the tops or the hoods, which is about the same as a flat bar, and the drops will save your butt on windy days. If you are seriously thinking about commuting 60 miles RT, I wouldn't consider anything but drop bars. The key to making drop bars work is to choose a frame/fork/stem combination that will allow you to raise the handlebars high enough. Lots of roadies never use their drops because the drop is too extreme and they can never get comfortable in them, but if you start out with a higher bar they work as intended.

It sounds like you've never really ridden a road bike, or at least not one set up right for you. A road bike that fits correctly you should be the most comfortable option for riding those kinds of distances. How do you think those racers ride 100-150 miles a day? The other thing is if you are putting in that kind of mileage you will adapt to riding in a more "roadie" position. Finally, get some reasonably light, nice rolling tires like Michelin Krylions if you plan to ride those sort of distances. That can make all the difference in the world.