Putting it in an extra room is fine if the room is big enough. A barbell is a little over 7' long and it's good to have a couple of feet clearance on each end to load it. You can make a platform for deadlifts that will protect your floor. It will be plenty loud on a wood floor but it will not harm the floor as long as the platform is thick and all the wood below is sound.
Most people with garage gyms don't have room for gym equipment inside the house.