It may not be the fastest but it seems like a good strategy is:
Tank or healer = Duty Finder (first time Guildhest and grind dungeons, not the fastest xp but good loot and you l2p your role a little)
DPS = quests and FATE grinding (fastest way to level but no loot and mostly boring zerg, learn little about party play)
Crafts = GC turn ins and guildleves.
I did quest stuff on tank/gld/pld so duty finder was instant pop but if I would have to do it over again I would probably do story quest as DPS, endure the duty finder queue as DPS one time (or beg FC) to advance the story then rerun grind the dungeon in the future when leveling a tank or healer for xp and lewt.
Quite frankly I find FATE parties to be boring after about an hour and like to change it up with dungeon grinding (I wish dungeons gave more xp but I'm not complaining). Since it is so easy to get groups as a tank or healer it seems like it makes sense to level in dungeons as those classes and save the quests and FATE grinding for the lower demand DPS classes.
Anyone else come up with similar strategies?