As to how you start other classes, yes, you go to that class's guild and take a quest from the receptionist there that unlocks the class. (Once unlocked, you switch classes by switching your equipped weapon.) There's no reason to wait until maxing out your first, though. You can add additional classes any time after your level 10 class quest on your starting class. At the very least you should pick up Arcanist and Thaumaturge at some point, probably by the time you hit 30 as CNJ. In order to become a White Mage, you'll need both CNJ up to level 30 and ACN up to level 15. And White Mages can bring in cross-class skills from both ACN and THM.

As to whether you should add other classes as well, it's mostly personal preference. You do get a 50% XP bonus when leveling secondary classes (applies on any combat class that's lower level than your currently highest level combat class). That's mainly to help make up for the fact that your highest class is usually the one you do the main scenario quests with, so your others won't have as many quests to get XP from.