I would suggest creating a general model of a character and then setting/fixing some parameters in a way that is verifiably "balanced enough" for whatever you're doing. In a single player game it probably doesn't matter. Final Fantasy 6, for example, didn't have balanced characters at all and it was really fun. What's more important in a game of that type is balancing the player characters against whoever you're fighting. Your ability to come up with characters that feel different and still have a sensible difficulty curve essentially depends on your ability to competently come up with role playing game mechanics in general. If you want to do this in an RPG Maker game or a Final Fantasy clone, you will have to pour over their mystical number formulas and try and figure out what they mean. It's probable that they don't mean shit, which means you're stuck making your game feel right by trial, error and creativity. You could maybe do some basic calculations on a spreadsheet like "number of hits to kill a thing, number of hits to win a battle, number of battles to level up, avg time per battle, battle time to level up" to make this faster for yourself. It might also help you come up with more boring variation balances equivalent to pokemon types.
If I was making a japan style fantasy RPG with ten classes, here are the classes I would choose:
Magician (the rabbits and tophat kind)
Ace Chef
Merchant (you always see these dudes but can never play as them)
Sailor (see above)
The King (serves no purpose other than increased difficulty setting. maybe tells joke.)
Unarmed Knight (wears armour, punches enemy in the mouth)
Girl (has the magic power to get kidnapped or suddenly have problems that are only resolvable by her male companions, cries, healing powers)
Time Mage (wears a cloak, takes self seriously, fights by striking people with pocketwatch)
Battering Ram Team (twice the people, half the personality)
Dog
Really, which fluffy descriptions you use for characters has very little influence on the way your game plays and quite a lot of influence on how your game feels. Consequentially, you should pick the most interesting sounding ones possible that are relevant to the theme of your game. Also if your game has a story with set characters, I guess that makes some of your decision for you. Using character classes is like using metaphor or simile or paragraphing, there's no set way to do it, and there's no best, ideal or global favourite way. How you use it depends on what you want to convey.
Given that you want to convey a sense of synergy between the characters in your party to emphasise the idea that they are bonding as they adventure, I suggest that you create synergy through individual deficiency. Start with blank slate, or neutral characters and then unbalance them such that each class has a flaw that another class can make up for. If players choose classes and you don't want any party to be better than any other party, you need to solve the problem of ensuring that any given party of n characters has as many flaws as any other possible party. The most trivial solution I can think of to this is that each class has a flaw made up for by each other class. This would make your game difficult unless the flaws were only minor, however. It also means a lot of work for you, because you need to invent 9 flaws and 9 advantages for each class.
The picture should have that relationship for each other class, but if I drew them in, I would have had a black circle instead. I have a gut feeling that you might be able to reduce down from this solution into a more manageable and elegant one with similar properties but I can't find a way to do it so for now, this can be treated as an idealisation of what kind of thing you might have to do. An approximate solution would be to pick a subset that sounds cool.