Since we will be going off this new "Armory System", I would like to assume one only needs to just equip specified weapon to take on the role of its class. With this in mind I really don't see quests to unlock new classes that they may want to add in future rather it be updates or expansions, unless doing said quest gives the new weapon as a reward. I'm sure it wouldn't be the only weapon of its type in existance and either bought in shops or NM drops.
For example in an expansion we're able to travel to some foreign land where Katanas and Sais are a common weapon from their culture. Go visit a shop, purchase weapon and equip to take on a new class. Same if killing a new NM and a new weapon drops. For example since Gunner isn't in the list of classes, this invading army in some higher level area drops guns, and this foreign weapon would unlock Gunner class. These are just examples not saying how it might possibly be, so basically what I'm saying is only requirement to unlock any class is to equip its weapon type.
There are tons of different weapons throughout the series and this being a game based on the "Armory System" I'd like to see most of them if not all. Harps, Daggers, Katanas, Guns, Shurikens, Whips, and Books just to name a few from past FFs. Not saying a class added for all these weapons be a lot of different classes that way, maybe too much, but I do like the variety of different weapons to use. Also if you were bare handed, would you still be considered Pugilist or No-Class?