In Final Fantasy III, the character stats are fixed, which means that leveling up jobs won't affect your base stats at all. Only HP grows when your character levels up; however, the job you are using affects how much HP the character can gain.
The job that provides the highest HP growth is Black Belt.
To guarantee that you can max out your HP (cap at 9999), you'll have to start leveling up as a Black Belt from character-level 40.
So if you care about the perfect game, you should start leveling up both jobs and characters here in front of the Ancients' Maze. Once you are strong enough, move on to grind levels in the Crystal Tower.
Grinding Strategy
- Change everyone's job to Black Belt.
- Black Belt is strong when fighting barehanded, so do not equip weapons on them.
- Use your Invincible to heal when your HP is low.
- Once you are strong enough to one-shot most monsters, you can buy Hi-Potions, then move into Crystal Tower for more powerful monsters (more EXP).
- Cheat: in Pixel Remaster, you can adjust the EXP multiplier, which dramatically increases EXP and saves you a lot of time.
Inventory -> Configuration -> Boost, then adjust the multiplier as needed.
You don't really get anything from maxing out all jobs. The Management Laborer achievement only requires you to level up one job to 99, which can easily be done with the White Mage from the beginning of the game.
Jobs don't grow with EXP, but rather with Action Points (AP). You get 1 AP when you perform 1 action. So what counts as actions? Any command you use during a battle counts as an action. For instance, selecting "Attack", selecting "Guard", or using "Magic" - these are all actions.
In a battle, you can level up your job only one time, which means that in order to max out one job, you have to fight at least 99 battles.
The best location to farm job levels is the grassland between Altar Cave and Ur. You don't need a powerful monster - one Goblin is enough.
Start by changing everyone to the same job so that they can level up at the same time. Put everyone in the back row to reduce damage, then start running around the grassland. Once the battle starts, everyone uses "Guard" for the first round; this counts as 1 action for each character. Then press the "Auto Battle" button for the number of actions needed. For example, if you need 7 actions to level up, you can guard until round 6 and kill the Goblin at round 7.