[@Cu Chulainn], before I forget to mention, the only difference I would see plot and forward with the character is that an Eldritch Knight has more options based upon their magical talents. Other than that, there is no real downside to staying with the barbarian aspect of it and pursuing a path of light through honor. Given you said you were taking Magic Initiate, as I recommend all players to do if they lack magic, this should proceed just fine.

The reason I say this is that all players receive a unique spell appropriate to their character. Having more access to it is in your best interest because it is yours.