7 Core Classes.

Saber
Servant of the Sword. Class Skills are high Magic Resistance(resists magic) and Riding(can ride stuff well). Requirements are using a sword, decent parameters, and they generally excel in burst damage.
Basically, if they use something you can call a sword and focus on hitting people with it, they go in Saber. Fairly straightforward.

Base Parameters:
Strength: A Mana: C
Endurance: B Luck: D
Agility: B

Archer
Servant of the Bow. Class Skills are Magic Resistance(resists magic) and Independent Action(allows limited action outside the mana reserves of the Master). The only requirement here is powerful projectile attacks or special projectile abilities, be they arrows, swords, bullets, missiles or dolphins.

Base Parameters:
Strength: C Mana: E
Endurance: C Luck: E
Agility: C

Lancer
Servant of the Spear. Class Skill is Magic Resistance(resists magic), being the only Knight with one Class Skill. Requirements are high Agility, and they specialise in hit-and-run attacks utilising their high speed.
If they're using a longer melee weapon(spear, lance, scythe, oversized dart) and using its range to keep out of the other guy's area, they go in here.

Base parameters:
Strength: B Mana: D
Endurance: C Luck: E
Agility: A

Rider
Servant of the Mount. Class Skills are Riding A at minimum (Can ride stuff except Divine and Phantasmal Beasts) and Magic Resistance(resists magic). Requirements are having ridden some form of mount; these mounts generally make up for lower Parameters.
If they have a particularly notable thing they rode, be it an animal, bike, giant robot, et cetera, they can be thrown in here.

Base parameters:
Strength: D Mana: C
Endurance: D Luck: E
Agility: B

Caster
Servant of the Spell. Class Skills are Territory Creation(allows creation of an area advantageous to their magic) and Item Construction(allows construction of magical items), though there's precedent for waiving either of them. The least straightforward of the Core Classes in terms of qualification, as it seems to act as the dumping ground for stuff that doesn't fit elsewhere.
Broadly, you can probably split the qualifying Servants into two: Magi and Creators.
Magi are the obvious qualification category; those who are known for their utilisation of magic and sorcery neatly fit in. The Creator category covers the Bookcasters; those known for creating something, such as books, art, or apparently solutions to crimes can also fit in here.
To TLDR: Magic-users, authors, artists and scientists, and probably the easiest Class to shoehorn people into.

Base parameters:
Strength: E Mana: A
Endurance: E Luck: B
Agility: C

Assassin
Servant of Killing. Class Skill is Presence Concealment (hides presence as a Servant until attack). Requirements seem to have slowly got looser; I'd say "Suprise attacks", but an executioner apparently also counts. If their legend is in non-battlefield killing, they probably qualify; those with their legends in espionage also qualify.

Base parameters:
Strength: D Mana: E
Endurance: D Luck: B
Agility: B

Berserker
Servant of Madness. Class Skill is Madness Enhancement(boosts parameters in exchange for sanity). Requirements, unsuprisingly, are anecdotes of madness in their legend; while both battle madness and bouts of insanity counts, the definition of 'madness' is extremely loose, apparently including "You must be mad" given Nightingale. The only Class you can canonically shoehorn people into.

Base parameters:
Strength: C Mana: E
Endurance: D Luck: E
Agility: D