My "basic D&D" races will probably wind up looking something like this:
Roll 3d6, in order (good old 2e style "Ironman" method of attribute generation). If you want to play a human, you don't have any special requirements. Pick a background and a class and go.
A dwarf requires CON 11+ (all dwarves are known to endure hardship and, paraphrasing Tolkien here, "make light of heavy burdens").
A halfling requires DEX 11+ ("hobbits are incredibly light on their feet").
An elf requires both DEX 11+ and WIS 11+ (to cover both the running/jumping/climbing trees/shooting arrows Legolas thing and the "what do your elf-eyes see" thing), and because of the extra requirement, the elf actually has a unique racial trait: elves are psychically sensitive to magic, so when they enter an area that's filled with magic or evil, they'll feel it (kind of a limited, DM-arbitrary detect evil / detect magic built into the character). This is a blessing and a curse, since powerful evil will make most elves nauseous (disadvantage on checks while in the area). (And now that I think about it, what if a high concentration of magic in an area makes an elf intoxicated?)
No darkvision, no low-light vision, no sensing secret doors, no sleep immunity, no speaka wit de badgers and moles, no fiddly little bonuses on anything. Mainly because those abilities are all either stupid or a pain in my ass when I DM a dungeon. I expect that when I implement this rule, I will see many human PCs at my table, a good number of dwarf and halfling PCs, and a respectably smallish number of elf PCs. Perfection itself.