I’ve created a version of my player quickstart just for Moldvay Basic D&D. I haven’t injected any house rules into this version, apart from the equipment packs, everything is completely rules-as-written. Click on the image or links below for the PDF and LibreOffice versions.
You’ll note there is some vague wording around the racial abilities like the Halfling’s ability to hide or the Elvish secret door detection – that is because if you’re a player, you don’t need to know the specific mechanics of those abilities. The DM will roll secretly for their success or failure, and I thought it was clearer just to state the ability rather than the underlying mechanic (it also saves a line or two of space, keeping the quickstart to one page). As a new player, if you really want to know, you can always look in the rulebook, but it won’t change the way the game is played.