All three routes are pretty much the same time-wise, however it all depends on you preference:
- Flagstaff to Shiprock, NM is a long drive across the Indian Reservation and is about the same time-wise if you live on the west side of Phoenix
- Flagstaff to Gallup is the easier drive in my mind because you are on Interstate all the way. If you live on the west side this is a great option
- Payson to Holbrook is a pretty drive and shortest if you live on the east side of town.