There's not enough quests to level each class to 50 so you'll have to do some of the other methods. (Dungeons, FATEs, Hunt Logs, Levequests, Daily Quests)

Most people focus on one class initially so they can get to max level and do the high level content that's available, but I don't know if that's necessarily a big motivator for you or not. At the very least you'll want each class to 15 to unlock Jobs for each class, and if you have nearly every class to 34 you'll have access to each cross class ability as well.