I don´t think that would play out. If you would see the possible candidates with their backgrounds + equip you would simply choose the strongest best equipped guys. This is not the way it is intended to be. You shall start with imperfect men.
But what I would welcome is being able to choose how my starting 3 look. You can already choose the names of your mercs, which is nice to have, but you are stuck with their faces :D While I think it is easy to get another name just by calling yourself with another name it is hard to get a different look.
So my suggestion would be to let the player choose how his starting brothers look completely with no limitations if he so wishes, but let him choose only beards and hairstyles afterwards for them and any other mercs he might hire. So the player gets more customization while it stays relatively realistic in the actual game.
-Wish I could get my hair back with just a click xD-
"I am a Paladin!"
>OMG, Malthus, there are no damn paladins in Battle Brothers...<
"OK, OK! Then I´m a wrecked down minstrel drunkard pretending to be a paladin, singing so wrong in the midst of battle that even the undead run in fear... Better?!"