Originally Posted by
Taika
Each class / job get their own class / job quests and hunting logs, so when you start a new class they will be there for you. However, you won't get new main scenario or side quests to replace those you've already done. People usually recommend only doing main scenario and class quests to level your first class as they alone can take you to 50 and saving all side story class exp for other classes when possible.
For new classes you can use hunting log, class quests, dungeons, FATEs and side quests to level them. After the dungeon exp boost that might be the fastest way.