If you want all the old school stuff with the modern ways of doing things....
Just play 5e with these limits:
Humans - can be Fighters, Clerics, Rogues, or Wizards.
1/2lings - can only be Fighters
Dwarfs - can only be Fighters
Elves - can only be be MC Fighter/Wizards. They must meet the MC restrictions at 1st lv, they begin with both classes at lv.1, and as they advance they must divide their xp in two & split it between their two classes (essentially it takes an elf double the xp to lv up as they're supporting two classes)
There are no other classes, there are no other races, there are no other race/class combos and other than with Elves there's no MC allowed. And Tasha's is not allowed.
No other changes to 5e.
There, I've saved you from having to read through about a dozen things all trying to copy the old stuff. Or having to rewrite the attack & save charts if you just pulled out the actual old stuff.
This is similar to some ideas I've had about making an OSR 5E.
I would add...
Eliminate cantrips. Light becomes a 1st level spell that allows blinding a foe.
I've also considered the idea of taking 'advanced classes' and redesigning them into subclasses of the core. For example Ranger becomes a Fighter subclass.
Honestly, though. It is better to start with a ruleset closer to what you want. You can hack 5E down and throw out 80% of the game to get what you want. Or you can start with a game that is 90% there and add a few tweaks.
In the end I've reached the conclusion that old-schooling 5E is a lose-lose proposition.
1. It takes a considerable effort to take 5E and modify it to suit an old-school style play. The base assumptions of how spells work and many other elements are completely different than an old-school game. There is a lot more than just limiting classes and races. You have to look at game rules, death and dying rules, spells, abilities as levels advance and apply changes to suit the old school style.
2. At the same time, you are changing 5E to the point that it is barely recognizable. You can sell your Old School 5E to potential 5E players, but what you end up presenting can be so far from what a 5E player expects that you are falsely advertising. The ONLY reason one would want to make 5E old-school is because one wants to attract 5E players. But in making 5E old-school one presents a ruleset that would not appeal to the 5E player.
The better solution, in my opinion, is to just offer to run an old school game. Advertise your old school game to 5E players. You'll probably get a hard-pass, often, but you may also get some people who are into it and you may get some interest from those who are curious.