You probably should go back to your main city and pick up the MSQ. That unlocks most of the quests (and dungeons and such) in the game. It'll lead you from place to place. Unless your level is too low for the current quest, you shouldn't have to do fates or leves at all. You have to do the MSQ. You have to. Riding skill, most of the dungeons, etc. are locked behind that.

As for your BLM, you do need thm at 30 and archer at 15. The actual stats they use doesn't matter. The more important thing is the cross class abilities you get from archer and arc. Before you get a job (which is what BLM is), you can pick and choose from all the classes but once you get the job, you can only get stuff from archer and arc. Also, your thm will continue to level the same as your thm but the other two won't. All the jobs are like that. You need the main class to be 30, the secondary class to be 15, and you get a third supporting class that doesn't have to be any level.