The Wizard ...

... _and like all the dashing heroes, is basically third level_

Class Features:

• Hit Dice: 3d6
• Hit Points: 12 + 3 * Con modifier
• Spells: as third level wizard (see PHB). Casting additional spells beyond the spell slot limit costs 1 hit point or ability point per spell level. Cantrips count as level 1. Rituals vary.

• Armor proficiency (roll d6): 1–4: none, 5: leather, 6: all light armors,
• Weapon proficiency: dagger, staff and (roll d6) 1: slings, darts, light crossbows, 2: pistols, 3: rifles, 4: short swords, 5: maces, 6: axes and pole arms,
• Tools: calligrapher's kit and (roll d6) 1: alchemist's kit, 2: dentist's kit, 3: gunsmith's kit, 4: archaeologist's kit, 5: doctor's kit, 6: herbalist's kit,
• Saving Throws (roll d6): 1–3: Int and Wis, 4: Int and Cha, 5: Wis and Cha, 6: Int and Con
• Skills: as per PHB

Starting abilities:

1. Opening the Valves of the Soul (arcane recovery) - every short rest cast 3 hit points worth of spells for free,
2. Spell Slots (restored per long rest): Cantrips: 4, 1st Level: 4, 2nd Level: 2
3. Choose an arcane school: 1: soul magic, 2: forced magic, 3: biomancy, 4: skin changing, 5: arcane polytech, 6: black magic

Soul Magic (similar to enchantment)

1. Hypnotic Gaze (as PHB 117),
2. Starting spells: Minor Illusion, Charm Person, Disguise Self, Illusory Script, Tasha's Hideous Laughter, Hold Person

Forced Magic (similar to abjuration)

1. Arcane Ward (slightly modified from PHB 115) - lasts for a day, has 6 + Int modifier hit points, regains 1 hit point for every ability point you spend to cast a spell,
2. Starting spells: Blade Ward, Mage Armor, Magic Missile, Jump, Tenser's Floating Disk, Knock, Shatter

Biomancy (similar to cleric's healing magic)

1. Disciple of the Biologician (as Disciple of Life, PHB 60) - every healing spell restores an additional 3 hit points, every healing spell not cast as a careful ritual has a 5% chance of causing a mutation,
2. Channel Life Force (similar to Channel Divinity: Preserve Life, PHB 60) - once per long rest you can channel life force (15 hit points) from one subject within 30 feet to another three subjects. You can restore any subject to no more than half of its hit point maximum. Unwilling subjects get a save.
3. Starting spells: Cure Wounds, Lesser Restoration, Enlarge/Reduce, Aid, Spider Climb, Spike Growth, Poison Spray

Skin Changing (polymorphymancy, similar to a druid's shapechange abilities)

1. Wild Shape (as Druid, PHB p. 66), transform into a 1/4 CR beast twice per short or long rest (e.g. wolf)
2. Regenerating Beast (partly as Druid Combat Wild Shape, PHB p. 69), while a beast, use bonus action to expend one spell slot and regain 1d8 hp per level of the spell slot expended. An expended cantrip restores 1d4 hp.
3. Starting spells: Thorn Whip, Goodberry, Animal Friendship, Disguise Self, Expeditious Retreat, Enlarge/Reduce, Enhance Ability,

Arcane Polytech (similar to ... well, not sure, conjuration and transmutation I guess)

1. Minor Conjuration (as PHB 116) - summons up a small object within a few meters,
2. Arcane Snake (as Poisonous Snake, PHB 308) - you possess an organized-matter snake-like projection, which you can give basic commands. AC 13, hp 2, Speed 30, +5 bite 1 damage, Poison DC 10 Con (2d4/half).
3. Spells: Mage Hand, Find Familiar*, Alarm, Grease, Blur, Cloud of Daggers, Heat Metal

... and then eventually you level up (sort of):

1. +1 proficiency,
2. gain 1 hp,
3. gain 1 hp,
4. gain 1 hp,
5. gain 1 hp,
6. gain 2 hp,
7. improve 1 ability score by 1,
8. improve 1 ability score by 1,
9. +1 cantrip spell slot,
10. +1 1st level spell slot,
11. +1 2nd level spell slot,
12. +1 3rd level spell slot,
13. +1 3rd level spell slot,
14. reduce cost of one spell by 1,
15. gain new skill,
16. become expert in existing skill, 
17. learn new weapon,
18. learn new armor,
19. gain one feat,
20. gain a 6th level ability.

What is your spell book?

1. a pliomastic memory implant (overclock once per long rest to +2 to Int for a day, then -4 to Int until end of next long rest),
2. a weird-silk quippu (can read and use for rituals in complete darkness),
3. an intelligent weapon or implement (it whispers the spells back to you when you sleep),
4. a regular manskin-bound tome as used by the divyak shamans (divyaks will like you better),
5. a proper tsarist tome from before the breaking of the Golden Reign (tsarists will nod and like you),
6. a crystal ball that plays back your spells (you can throw it as a grenade for touch effects, it won't break, don't worry).