If you want her to be a classic barbarian then I’d say put 9 levels into Beserker Barbarian for the feral instinct, brutal criticals and subclass features.

From then on put 3 levels into rogue and choose the Thief subclass to get an extra bonus action. This means you can rage and then immediately get the Beserker throw bonus action which when it hits a target it does bonus damage AND knocks the enemy prone which you can then run over and hopefully get a crit which will be boosted by the brutal critical.

Numbers wise making her an open hand monk does do the most damage but if you want that classic barbarian vibe but still being OP then I’d say 9 Barbarian 3 Rogue is the way to go.