All races are equally good from a narrative standpoint, depending on your narrative. PCs from traditional barbarian cultures (e.g. full blooded orcs, Wild elves) might be narratively preferable in a game that allows them to contrast the merits and weaknesses of their strictly deontological ethics with the rampant pragmatic utilitarianism of the City.
PCs from traditional warrior cultures consistent with barbarism but with out specific preference for the Barbarian class (e.g. Moon elves, Githyanki, tabaxi) can also make interesting Barbarians from a narrative standpoint as their specific class choice will differentiate them from 'default' members of their race while allowing them to essentially affirm their society's core values. This is a very useful technique for making characters who happen to be extremely stereotypical (e.g. LG Dwarven Cleric of Moradin, CG Elven Ranger, etc) without them feeling like a 'default' character narratively.
PCs from cultures that aren't typically very war-like, but not particularly pacifistic either (most PC races) can make good barbarians by helping to remove race as a factor from the character's narrative, allowing the character to emphasize their own merits as an individual without NPCs or the play group being influenced by the character's choice of race with specific regard to class. This option on its own also helps a character to blend into the narrative background, which can be useful in balancing out a character that might narratively seem 'too extreme' or 'too plot-dominant' otherwise, or help in normalizing the character's position within a larger, non-barbarian organization. The benefits to a barbarian from these races are abstract and complex, to be sure, but they are no less real than the benefits from the other options.
PCs from cultures that produce Barbarians extremely infrequently and whose members tend to make poor barbarians, but which are not specifically opposed to barbarism (e.g. Halflings, most Small or Tiny races) can make good barbarians as their natural disadvantages at their chosen role provide them with insecurities and doubts as to their usefulness. Such characters often possess a need to prove themselves, which gives them a strong reason to go adventuring and lots of narrative options for their dealings with other characters (both PCs and NPCs) as their inherently unstable starting state almost necessitates character growth.
PCs from cultures that abhor Barbarism, especially pacifistic cultures such as the Ondonti, also have excellent narrative potential as Barbarians. Having abandoned the ways of the their homeland (e.g. because of the perceived lack of effort to save their enslaved compatriots) there is potential for scenes showcasing the surety or doubt the PC has in their decision and emotional confrontations with former allies.
So, basically, without knowing the narrative you want to tell every race is equally good.
Rage-filled lone warrior stories can be told with a wide variety of different main characters and be excellent because of the details of that main character and his or her journey, though the narrative itself will need to be very different depending on that character.
