Flat bars suck. Give me either north road bars or drops raised a sensible height any time. North road bars place your hands in a very comfortable position, and you can also lean forward onto the curves or straight middle section to cheat the wind a little. Drops give you four positions- the tops are the same as a flat bar, but you also have the rear curves, hoods or drops. Flat bars force you to put your hands in one not very comfortable position the whole time.

I'd look for an old British roadster. These came with a comfortable riding position and either single speed or a bombproof 3-speed IGH, and if cared for will last forever. Alternatively, most old '10-speed' road bikes can be converted to single speed fairly simply.