These ones are all pretty straightforward since IX is a more "traditional" fantasy setting and the party is a more stereotypical fantasy party, I'll only go throught a few of them though (I have no idea what Quina would be)

 

Zidane - Assassin, this one is fairly easy to explain since he's a thief yes thieves aren't assassins but they're both sneaky and both use daggers.

 

Vivi - Caster, even easier to explain; he uses magic

 

Steiner - Saber, two reasons his sword (obviously) and his knightlyness (he is sir rustbucket after all.)

 

Freya - Lancer also obvious as she's a dragoon.

 

Amarant - Berserker, this one's a bit more difficult however he strikes me as a berserker as opposed to any of the other classes.

 

I've left a few notables out as they overlap with the others, Garnet and Eiko would both be Casters, Beatrix would be a Saber and Kuja would be either a caster or a berserker.

 

 

 These are a bit more complicated as X strays away from the traditional fantasy party you get in IX

 

Yuna - Caster in X and fucking everything in X-2 (due to dress spheres) but would most likely prioritise being summoned as an Archer

 

Rikku - Assassin in X (same reasons as Zidane above) and like Yuna fucking everything in X-2 but prioritising being summoned as an Assassin

 

Tidus - Saber straightforward with his preference for swords.

 

Wakka - Archer, hear me out on this; his primary way of attacking is with his blitzball at range and considering some of the things Archers in the fate universe use Wakka being an one isn't that much of a stretch.

 

Kimahri - Lancer, although could also possibly be a cater but primarily a Lancer.

 

Lulu - Caster, straightforward and simple.

 

Again a few notables have been left as they overlap (Paine and Auron being the biggest two) this group was less straightforward to select for as they all have their own unique skillsets, I added Yuna in because (as far as I'm concerned) she's the main character for both games.

 

 

a little bit more complicated still and I won't go through all of them (just Lightning, Sazed and Fang as they're easiest) due to how that game's mechanics work.

 

Lightning - Saber although you could make an argument for her being summoned as a Caster, Rider or Archer however I think she'd primarily be summoned as a Saber.

 

Fang - Lancer but could probably be summoned as a Rider or Berserker but again primarily summoned as a Lancer

 

Sazed - Archer but again could be summoned as a Rider (yay for Gestalt mode on the summons)

 

Even more complicated than X due to the paradigm system and the fact that realistically every character can be a Rider and a Caster and if we take Lightning Returns and XIII-2 into account Lightning can be a Lancer as well (Serah would be an Archer while Noel would most likely be a Saber)

 

 

This one's mostly about the Warrior of Light but I'll go through the Scions based on the group at the end of Shadowbringers so a minor spoiler for that.

 

Thancred - Saber or Assassin, most likely Assassin though since I wouldn't know how the Fate classes would take his Gunblade into account and he's most notably a rogue for most of the game's storyline

 

Minifillia/Ryne - Assassin, she was taught to fight by Thancred afterall.

 

The rest are all Casters (although Alisaie could be summoned as a Saber since she's a Red Mage)

 

But the biggest one is the Warrior of Light, I'll go through each Fate Class and explain why the Warrior of Light fits as they could be summoned as all of them. I'll use my own WoL as the basis for this so lets go into it

 

Saber - Paladin, Samurai and Dark Knight (also Red Mage and Gunbreaker to an extent) exist as jobs that the WoL can have and has potentially mastered especially with my WoL having mastered Paladin, Samurai and Red Mage.

 

Lancer - Dragoon 'nuff said. With my WoL having started out as a Dragoon they'd probably be more likely to be summoned as a Lancer as opposed to other classes with the possible exception of Saber.

 

Archer - Machinist and Bard (also Dancer to a lesser extent) and my WoL has mastered both Machinist and Bard however is less likely to be summoned with them due to my preference for melee jobs.

 

Rider - All the fucking mounts you get, although would most likely be summoned with a chocobo as a mount.

 

Caster - Black Mage, Summoner, White Mage, Scholar, Astrologian, Red Mage and Blue Mage so many casters so little time although my WoL would be more likely to be summoned as a different class due to Red Mage and White Mage being the only two caster jobs that are at 80 and in Red Mage's case it would probably increase the likelihood of being summoned as a Saber.

 

Assassin - Ninja, although if the summoning of Li Shuwen is anything to go by Monk would also count. Even less likely to happen then Caster as neither of those jobs are at 80

 

Beserker -  Warrior and to a lesser extent Dark Knight. Although with the rules Fate has in its servant summoning it's possible to summon servant as a berserker but some are more likely to be summoned as a berserker naturally and Warrior fits that mould perfectly (as a classic berserker) although Dark Knight could also fit.