Dancing Hoskuld
Deity
Personally, I don't like the Appian Way as is, or as has been suggested by Koshling or Vokarya. I would prefer that it built a "straight Imperial Road" to the all the cities (and forts) nearest to your capital. Then from each of those the the cities and forts nearest them until you have a proper military movement network. I would also have it as a national wonder and have some way of having the roads built to new cities and forts. This is a similar idea to Koskling's route change suggestions. If it is going to be buildable then plots need a property that indicate that they are on the "straight" line between cities/forts and the construction of route types need that property.