Each class has their own hunting log, doing all of those plus the first couple of class quests will probably get you to 10 easily enough, then you can start work on the next batch of hunt log entries, do the available guildhests once each for the completion bonus, and just bash out some FATEs or levequests to get you the rest of the way to 15.

Also, you get a 50% XP bonus for any classes that are lower than your highest-level one, and you get bonus XP on guildhests for the first time completion on each class, so it's pretty quick to get new classes to 15 for the sake of meeting job requirements.