As someone who came to the OSR from 5E myself, I’d recommend B/X D&D (via either Old-School Essentials Classic Fantasy, Basic Fantasy RPG, or the original Moldvay/Cook Basic/Expert) as a great first foray. There is a lot that you’ll already be familiar with but still plenty of new-to-you stuff to be excited about.
If you’re going with OSE, I’d run Winter’s Daughter. (I just ran this adventure in OSE for a group that had only played 5E before, and they loved it.)
There are also some fun pegenerated characters in Rogues Gallery I for OSE (which could also be used with B/X, or with Basic Fantasy with some minor conversions).
For Basic Fantasy RPG, I’d go with The Blackapple Brugh (scroll down about 1/3 of the way to find download/print links). And here are some 3rd level pregenerated characters.
For B/X (or any of them) Tomb of the Serpent Kings is also a great choice, as others have mentioned. It’s great for teaching both the one running the game and the ones playing the game how to “do” OSR, or at least one version of OSR.
Honestly, you can run any of these adventures with any of these systems with minimal-to-no conversion, as they’re all pretty much just B/X D&D.
(Also, there are SRDs for both OSE and Basic Fantasy if you want to get a good read on them without having to buy/download anything.)
Keep in mind that much (if not most) of the character options/development in B/X (and most other OSR games, in my experience) comes from what happens in the game and not from the rules or character sheets.
Have fun!