I've not yet bred chickens (have worked with other animals though), but if I were going to I would go with "spiral breeding." Look it up; only thing is I think you'd probably do better with more than 13 chickens.
 
Agree that culling is very important. Produce a lot, cull a lot. If you really care about the breed you're working with, you'll accept nothing less than perfection. Especially if you plan on selling, you want your customers to get the very best.
Ruthless indeed! Yes, a god that plays favorites is not good. Nature is ruthless, it kills whenever animals show a moment of weakness. This is what keeps wild animals strong and healthy. We should act in the same manner with our domestic animals. When we don't, we end up with pug-faced bulldogs who can't breathe, collies that are afraid of sheep and other tragedies. The same thing could happen to chickens if people favor the wrong traits.
 
Treat each bird in an equal and objective manner, without favoring any over the other or compensating for weaknesses. And start with the best stock you can afford.