Unlike any other Final Fantasy games where your stats increase in a fix amount based on your character level, FFIII is a little different because of the Job system. As you see that we have a separate job level that influence how your characters grow which mean that your characters stats are very dependent. I will use this simple equation again to make it simpler to understand: 

Damage = character level + Job level

So the higher your job level the more damage you can deal, same with the character level. But in early game, you heavily rely on job level to boost your damage since job level is quiet easier to level up than your characters. I'll explain later on this.

Since your characters' stats are tied to job level, you can't really manipulate them, that means you can simply grind job level normally except HP. Now this is very crucial if you want to have 9,999 HP since it is the only stat you can manipulate. Let me explain how the HP grows. 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 provide 50 HP. 

Now you should figure out what is happening here, different jobs give different HP grow. So, what job provide the most HP grow to your characters? 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.

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:

• Bahamut's Lair
• Ancients' Maze
• Crystal Tower

Above 70:

• ??? Cave