Fates and dungeons are a good basement to level but dont forget your huntlog for your class (unlocked after first classquest iirc) that usually gives enough xp for 5 levels. Also Duty roulettes (guildhest from level 10 on, low level from level 16 on if atleast 2 instances unlocked) push a lot.
In Limsa you can also unlock the challenge log and the challenges for roulettes done, hests and fates give free xp that you dont want to miss out as well