Not sure if this is up your alley but I've had a weird idea of running an old-school style game using just the Basic rules with old school 'classic' class/race/background combos, something like
Fighter = human, fighter class, soldier background
Cleric = human, cleric class, acolyte background
Wizard = human, wizard class, sage background
Thief = human rogue class, criminal background
Then for the demihumans:
Dwarf = mountain dwarf, fighter class, soldier background
Elf = high elf, fighter class, sage background (to mimic the old mage/fighter split of old school elves)
Halfling = lightfoot halfling, fighter class, criminal background (i.e. a fighting class with thiefy/sneaky elements)