If you're like me and you like to let the MSQ introduce you to new zones and get the full experience, I would advise you to stay away from Coerthas for now and instead go to Costa del Sol and grind fates there until you are 36. This along with your 3 hunting logs (class, job and company), your job quests (don't forget those!) and the duty finder should easily get you to 36 so you can continue enjoying the MSQ.

As a note, when you go back to Drybone to continue the MSQ you'll have to do Iliud's sidequest first, then he'll have the MSQ for you.