If you think they’d be from a smaller house, go with the Great House that that smaller house is sworn to (ex: House Manderly —> vote Stark)

They don’t have to be a nobleperson, they can be someone working for the house or being ruled by them. Roles could be a sworn-sword, a septa, a butcher, a blacksmith, or even a lowly peasant.

You can consider the region itself. For example, if you feel the character would be from Dorne, pick House Martell.

You can consider the personality of the character. For example, if your character is all about honor, then consider either House Arryn or House Stark.