And this thread shows why the floating ASI are a mistake. They remove flavour from a race and the minmaxer will still only play certain combinations because now the racial abilities determine what race is best for a class.
Much was lost and nothing was gained.
Oh the irony.
5e(2014) had only very few viable races for min/maxers for each class.
Barbarian was either a Half-Orc or a Shield Dwarf.
5e(2024) allows you to choose any race without compromising your stats and Min/Maxers will choose the race whose features compliments their preferred play-style.
As for the OP's question Half-Orc or Dragonborn would likely be my choices for the Barbarian mostly because they would make cool looking Barbarians.