The dog playpen I use has a fine net top so that is dust filter #1.
I use alfalfa hay in the brooder not shavings dust helper #2.
I use a stand alone dust filter near the brooder I think it is an ionic breeze, dust helper #3.
Really if you couldn't hear chicks you'd never know they were here.:)
I brood in the living room in a dog playpen.
The mess is minimal if done correctly and the chicks bond to me first so that makes integration later easier since pretty much all the chickens out there were done this way .:)