You will find that we are all different, with different goals and set-ups. Many of us would never dream of brooding in the house, but others would not do it any other way. I like staying married so, considering the dust, I will only brood in the coop.
I put my brooder in the coop from Day 1. It is a 3' x 5' so it is reasonably large. I keep one area in the correct temperature range but let the far corners cool down, often 20 to 30 degrees cooler. I find the chicks usually spend most of the first two days in the heated area, but by the third day they are playing all over the brooder. They come back to the heat when they need to warm up, which is not really all that often, and they normally sleep in the heated area. This way, I do not have to worry about keeping the entire brooder the right temperature, but let them find their own comfort zone.
The biggest problem I find brooding in the coop is arranging the heat when I have adult chickens present. I built sort of a chimney thing to hang the heat lamp through and allow me to raise and lower it a fair amount, but I have limits on how high I can raise it. It does protect it from the adult chickens. This results in the heated zone being warmer than it needs to be during the latter part of brooding, but they have plenty of room to get away from the heat so they do fine.
I do worry about heat lamps and fire. Be sure it cannot fall. Throw that clamp away so you are not tempted to rely on it and use wire, chain, something secure, to hang it with so it cannot possibly fall if you use a heat lamp.
