Basement shop

I’ve started to frame up a wall in the basement to closing in a woodworking room since it was left unfinished and open. The dust go everywhere and would get to the furnace and blow throughout the house.
I’m reading about how to soundproof the room so the running saws and dust collection wont disturb anyone watching TV that’s right above the room. I also want to make it more quiet if someone were watching TV in the rest of the basement. I basically have to make a floating ceiling with floating walls so the noise and vibrations will hit the drywall and stop from going through the framing and out the other side or up through the floor upstairs.
I’ll post more pictures to explain, it’ll be interesting to go back later and see if what I’m planning will happen.