Maximum Stats
The way stats work in FFII is very different than others. You have two factors that help grow your characters, they are Character Level and Job Level. Character level grows your overall stats while job level grows your HP. Because of this, you cannot control how you grow your stats, the only thing you can manipulate is your HP. In order to achievement the maximum stats is have your HP max at 9,999.
HP grows when your character levels up, but the amount of HP depends on the current job your character is using. For example, If Warrior raise 70 HP, White Magic only gives 50 HP. Now the question is what job provide the highest amount of HP when a character levels up? It's Black Belt, follows by Viking.
To guarantee that you max out HP, you must level up as Black Belt from character level 40. This means that if you characters are already level 60 and start leveling up as Black Belt, you cannot have 9,999 HP.
For more detail visit Perfect Game section.
Character Level Grinding
Unfortunately, You can only obtain Black Belt from the last Crystal (Earth Crystal) at the very late game (Ancients' Maze). It kinda put a restriction on you that you must play through the game below level 40 until you get the Black Belt to start leveling up. Fortunately, it's not too hard.
Here are a few spots where you can leveling up based your level, here they are:
Level 40-70:
Level above 70:
Job Level Grinding
Job doesn't grow with EXP, but rather Action Point (AP). You get 1 AP when you perform 1 action. So, what counts as actions? Well, any command you use during a battle are all counts as actions. For instance, you select on "Attack", you select "Guard", you use "Magic", these are all actions.
In a battle, you can level up your job only one time which mean that in order to max out one job, you have to fight at least 99 battles.
For table reference of many actions you need for each job, you can visit Grinding Job Level section.
Farming Strategy
The best location to farm job level is the grassland between Altar Cave and Ur. You don't need a powerful monster but a 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 the damage, then start running around the grassland. Once the the battle, everyone use "Guard" for the first round, this will count as 1 action for everyone, then press the auto battle button for number of actions needed. For example, if you 7 actions to level up, you can guard until round 6 and kill the Goblin at round 7.
Watch the video below: