It will be a lot of personal preference, really, as you could use anything from a tri bike to a hybrid. Being in Ohio I'd assume you'd want fenders (maybe), so eyelets would be good. Rack mounts aren't necessary unless you want to mount one, so that's up to preference.

As usual with bikes, the biggest factor is fit, and in this case the importance is magnified because of the distances. Do you just want a randonneuring frame for the style (nothing wrong with that btw) or will it be a rando bike in real life?