Classes for an ItO-esque system.

So here's the deal for a stripped-down system I'm looking at hacking together. Largely inspired by Into the Odd.
You roll your six stats in order as normal. You can 'invert' them if they suck, so a 3 becomes an 18, etc.
Your class is determined by your best stat. If there's a draw, you get to pick between them.
Strength = Fighter (you all know what a fighter is)
Dexterity = Expert (covers thieves, rangers, doctors, assassins, etc etc. All the 'skilly' characters)
Constitution = Survivor (basically the dwarf/halfling, with big defensive bonuses)
Intelligence = Magician (vancian casting from a spellbook).
Wisdom = Cleric (small list of known miracles, pray and hope your god grants the prayer).
Charisma = Psychic (always-on minor supernatural abilities that /just work/).

All classes get a d6 hit-dice.

Each class has a benefit or two for their class.
Fighters add their level to rolls to hit and damage, and get to follow through as many times per round as their level (follow through = if you drop a victim, you can make another attack immediately).
Experts get a 'second chance' on skill rolls (IE roll-under-attribute) rolls. If they get their level or less on a d10, they succeed. They get to make this d10 roll even when normal humans can't roll at all (climbing without handholds etc). They pick one area of expertise (like stealth or medicine or outdoorsmanship or whatever) and roll their second chance for that on a d6.
Survivors get a flat +5 hitpoints at first level. They add +5 to their saving throws to avoid bad stuff. They get to pick one area (like running away or spelunking or whatever) and have a second chance on skill rolls there like an expert.
Magicians cast spells. (Spells don't have levels). You start with two spells in your spellbook and memorize them vancianly: you can have as many spells as your level memorized simultaneously. There's a big d30 list of spells including a lot that are like 'protection from ...' or 'charm ...' that roll a bunch of different spells into one template, where the magician picks what it applies to when they pick the spell. Experimental magic like casting spells weirdly or copying from somebody else's spellbook has a chance to cause fuckups (from a big table).
Clerics know the following miracles: Cure Sickness, Cure Wounds, Detect Unholy, Sanctuary and Turn Away Unholy. (unholy is undead, and also demons, worshippers of evil powers etc) (sanctuary blesses a victim so that enemies must save in order to be able to attack them). To cast a miracle, the cleric must roll their level or less on a d6 (6s always fail). If they succeed, the miracle happens, if they fail there is instead a complication as divine forces pay attention to them and make demands.
Psychics get a minor supernatural power from a big d30 list. It always works. Stuff like creating/controlling shadows, being able to move things without touching them, having a mesmerizing gaze. Freeform improv what you can do with them, with some guidelines for the GM (numerical/mechanical effects scale off level. So a first level psychic using their power to attack does 1 damage, etc). Get double the effect by taking d4 damage and risking a magical fuckup, triple for taking 2d4 damage and a fuckup, etc.

Once you've picked your class, your starting gear is picked off a table comparing your best stat (the one that determines your class) vs your HP roll. Same as how ItO does it.
I'm thinking this table maybe also generates your starting spells/powers/chosen skill as well.