Vaan Shikari (Zalera) - If anyone is going to be a Shikari, it had better be Vaan. Shikari is something I was wanting to use in one of the teams, and no one is better at it (particularly at abusing speed), making Vaan the obvious choice. Zalera gives him an extra 435 HP for more durability.
Ashe Knight (Belias, Mateus) - Like Vaan and Shikari, there is no one better at being a Knight. Why Knight in this party? Because it fit with the other Esper choices. She gets an extra Potion Lore as well as Curaga, Regen, Esuna, and Cleanse, helping her fit into a backup healer role when you need it.
Balthier Red Mage (Zeromus, Zodiark, Shemhazai, Cuchulainn, Exodus) - Red Mage is definitely master of none in FFXII, but it does get fairly potent with the right Espers. Except for Vaan, his stats are the most well rounded for this role. He gets another Channeling, Esuna and Cleanse, the -ga elemental spells, can wear some degree of heavy armor, and gets Ragnarok as a choice in weaponry.
Fran Breaker (Ultima, Hashmal) - Vaan fills every role perfectly it seems, so many choices are the second best in all honesty... Fran fits perfectly into Breaker. Ultima and Hashmal giver her the necessary Swiftness licenses to keep up.
Pennelo Uhlan (Famfrit) - Uhlan is another jack of all trades type character, but it is much more focused on melee than Red Mage. Solid fighter. Famfrit gives her an extra Potion Lore in case things go bad.
Basch White Mage (Adrammelech, Chaos) - Interestingly enough, he makes the (second) best White Mage. (Damn you, Vaan!). His MP is kind of low, but an extra 310 HP, a Battle Lore, Souleater, and the Defender make him a good Souleater spambot when he's not healing. The backup healers (Knight and potion abuse) help make this possible.
I have written down "Blok 20,5,5", but I don't remember why exactly. I think it gets you another Maximillian?
Vaan Monk (Ultima, Zodiark, Chaos) - Like Shikari, if you're going to use a Monk, you should do it right. Ultima gives him two much needed Swiftness licenses to make him a beast. Equip poles for dealing with defensive enemies or bare knuckle box any wimps. Chaos and Zodiark give him Holy, Esunaga, Protectga, Shellga, and Renew, if you really really need him to be a backup caster.
Ashe Samurai (Belias, Exodus, Zeromus, Cuchulainn, Zalera) - This is probably the one and only scenario in which Vaan isn't the best at something. Ashe is. She gets Libra, an extra 500 HP, Stamp, a Magick Lore, and access to the Blood Swords if you want to abuse them instead of the one-handed Masamune. She can do a lot of things, but she's best at spamming physical attacks and your motes.
Balthier Black Mage (Adrammelech, Mateus, Hashmal) - Anyone except for Basch and him are a waste of potential as a Black Mage. The three espers give him access to bombs, including the strongest in the game.
Fran Machinist (Famfrit) - Machinist doesn't really use Strength or Magic much... making Fran the obvious choice. (Poor Fran.) Famfrit gives her much needed Warp, Vanishga, Slowga, Reflectga, Hastega, and Graviga, which is the closest you can come to a Time Mage without the suck.
Pennelo White Mage (-) - In this case, the choice was to abuse her highest MP of the party for heal spamming. Considering only one member of the party has heavy armor, you might need it... The espers were all better off with someone else.
Basch Archer (Shemhazai) - Shemhazai allows Bash to equip the best heavy armor in the game, turning Archer into a beast.
I have written down "Stok 25,1,1" but I don't remember why.