I know what you mean. You will find varying opinions and then have to decide what to do for yourself. I don't have pesky snakes around here, so I haven't even tried to figure out how to keep them out of my pen. I think if you use 1/2" hardware cloth around your chicken run and coop, that would keep the snakes out of that area, but this wouldn't solve any free range time. Free ranging comes with risk.
I brood my chicks in my garage under super safe conditions until they are 8-10 weeks old. Then I put them out in a run and coop adjacent to my main run and coop for a month or two. They are nearly full sized before integration with the big girls.
In my brooder right now I have 3 chicks that are 4 weeks old and 1 that is 3 weeks old. They have been together since the beginning. I actually got the 3 older ones to help the lone egg hatch. They have gotten along well and I think that little one is going to end up quite tough because she is always trying to keep up.
Your original question was what the difference was between a brooder and a brooder house. If now you are asking how to integrate, I would suggest just giving it a go. they are not far apart in age.