Here's my design take on a HP-style Magic set, before Strixhaven shows me how it's done.
First, I think the Houses are a must: Oxhoof (GR) Houndhug (WG) Owlsight (UW) Drakecharm (BU) Phoenixspark (RB)
Then there's the mechanics: Study and Brew.
Early Class2U
Enchantment (U)
At the beginning of your upkeep, you may study. If you do, draw a card.
(To study, pay 3 or discard a card.)
Drakecharm Duelist1B
Creature - Human Student
Whenever Drakecharm Duelist blocks or becomes blocked, you may study. If you do, Drakecharm Duelist gains deathtouch until end of turn.
2/1
Overschool Mentor2B
Creature - Vampire Student (U)
Once per turn, if you would study, you may pay 1 life instead of its normal cost.
3/2
Eager Oxhoof2R
Creature - Human Student (C)
Whenever Eager Oxhoof attacks, you may study. (To study, pay 3 or discard a card.)
Eager Oxhoof has +1/+2 if you studied this turn.
3/2
Practical BoltR
Instant (C)
You may study (To study, pay 3 or discard a card.)
Practical Bolt deals 1 damage to any target. If you studied this turn, Practical Bolt deals 3 damage to that target instead.
Karinda Gel, Spellhoarder2UU
Legendary Creature - Human Wizard (R) U: You may study. If you do, Karinda gains Hexproof until end of turn.
At the beginning of each end step, if you studied this turn, draw a card.
3/4
Experimental PetB
Creature - Rat (C)
Menace
Sacrifice Experimental Pet: If you studied this turn, draw a card.
1/1
Healer's ClassW
Enchantment (U)
At the beginning of your upkeep, you may study. If you do, gain 3 life.
Sacrifice Healer's Class: If you studied this turn, creatures you control gain indestructible until end of turn.
Now for Potions, there's the Brew mechanic:
Musclemax Potion6G
Artifact
Brew (This spell costs 1 less for each different name among ingredients you control. Basic lands count as ingredients.)
At the beginning of your combat step, put a +1/+1 counter on target creature you control.
Pack-your-things Concoction5B
Instant (R)
Brew (This spell costs 1 less for each different name among ingredients you control. Basic lands count as ingredients.)
Exile target creature and all artifacts attached to it.
Polymerize Potion5U
Instant
Brew (This spell costs 1 less for each different name among ingredients you control. Basic lands count as ingredients.)
Create a 1/1 blue Student creature token. Then a creature of your choice becomes a copy of another creature of your choice until end of turn.
Wortleg AnuranBB
Creature - Toad Ingredient (C)
Whenever you cast a spell with Brew, each opponent loses 1 life.
2/3
The idea of "Studying" is interesting, but I'm not sure the action is right. It almost feel like studying should be skip your combat phase.
Brew will be hard to balance, especially if you are counting basic lands as "ingredients". I think you are better off removing the basic land part and having more cards like the frog that do things when you Brew, then it feels more like you're actually mixing some stuff up to make a new thing. You might also consider, rather than a cost reduction, making it like Spell Mastery where the spell gets an added effect if you have some number of ingreditents (2 or 3 probably)
I don't like basics being "ingredients". Just feels more like a domain style concept. UNLESS you make ingredients also. Like an artifact that costs 2 and acts as an ingredient and taps for a colorless Mana. Kind of like a less powerful Mindstone. There could also be creatures, instants, and sorceries that put an ingredient token on the battlefield.
Aspiring Spike 3WG
Legendary Creature - Human YouTuber
Brew
If ~ cost 2 or less Mana to cast put 2 ingredient tokens on the battlefield.
3/3
Cookbook. 2
Artifact - Ingredient t: add C.
About Study. Wow I like not attacking to study. That is a pretty great idea.
First, I think the Houses are a must: Oxhoof (GR) Houndhug (WG) Owlsight (UW) Drakecharm (BU) Phoenixspark (RB)
Then there's the mechanics: Study and Brew.
Early Class 2U
Enchantment (U)
At the beginning of your upkeep, you may study. If you do, draw a card.
(To study, pay 3 or discard a card.)
Drakecharm Duelist 1B
Creature - Human Student
Whenever Drakecharm Duelist blocks or becomes blocked, you may study. If you do, Drakecharm Duelist gains deathtouch until end of turn.
2/1
Overschool Mentor 2B
Creature - Vampire Student (U)
Once per turn, if you would study, you may pay 1 life instead of its normal cost.
3/2
Eager Oxhoof 2R
Creature - Human Student (C)
Whenever Eager Oxhoof attacks, you may study. (To study, pay 3 or discard a card.)
Eager Oxhoof has +1/+2 if you studied this turn.
3/2
Practical Bolt R
Instant (C)
You may study (To study, pay 3 or discard a card.)
Practical Bolt deals 1 damage to any target. If you studied this turn, Practical Bolt deals 3 damage to that target instead.
Karinda Gel, Spellhoarder 2UU
Legendary Creature - Human Wizard (R)
U: You may study. If you do, Karinda gains Hexproof until end of turn.
At the beginning of each end step, if you studied this turn, draw a card.
3/4
Experimental Pet B
Creature - Rat (C)
Menace
Sacrifice Experimental Pet: If you studied this turn, draw a card.
1/1
Healer's Class W
Enchantment (U)
At the beginning of your upkeep, you may study. If you do, gain 3 life.
Sacrifice Healer's Class: If you studied this turn, creatures you control gain indestructible until end of turn.
Now for Potions, there's the Brew mechanic:
Musclemax Potion 6G
Artifact
Brew (This spell costs 1 less for each different name among ingredients you control. Basic lands count as ingredients.)
At the beginning of your combat step, put a +1/+1 counter on target creature you control.
Pack-your-things Concoction 5B
Instant (R)
Brew (This spell costs 1 less for each different name among ingredients you control. Basic lands count as ingredients.)
Exile target creature and all artifacts attached to it.
Polymerize Potion 5U
Instant
Brew (This spell costs 1 less for each different name among ingredients you control. Basic lands count as ingredients.)
Create a 1/1 blue Student creature token. Then a creature of your choice becomes a copy of another creature of your choice until end of turn.
Wortleg Anuran BB
Creature - Toad Ingredient (C)
Whenever you cast a spell with Brew, each opponent loses 1 life.
2/3
Brew will be hard to balance, especially if you are counting basic lands as "ingredients". I think you are better off removing the basic land part and having more cards like the frog that do things when you Brew, then it feels more like you're actually mixing some stuff up to make a new thing. You might also consider, rather than a cost reduction, making it like Spell Mastery where the spell gets an added effect if you have some number of ingreditents (2 or 3 probably)
Aspiring Spike 3WG
Legendary Creature - Human YouTuber
Brew
If ~ cost 2 or less Mana to cast put 2 ingredient tokens on the battlefield.
3/3
Cookbook. 2
Artifact - Ingredient
t: add C.
About Study. Wow I like not attacking to study. That is a pretty great idea.