If you want to follow the story do the story. If you understand all quests are just exp to get you to max then do threads of fate. First thing go to each zone and get their story quest (it's just a bar you'll fill doing stuff in the zone including dungeons.) So that way you can queue for dungeons and have them all count towards one of the quests.
Plus threads of fate lets you get started on Anima early. And you can focus on the gear you want instead of having to wait for the right quest to offer it.