Brad, it's not expensive to stop the sound and the noise, all you need is earplugs or noise canceling headphones that would be the best option.
It gets expensive when you try to soundproof the room because the sound will travel through most solid materials and it will come out on the other side being as loud.
People who do sound systems, or make in-home theaters they have a saying" to soundproof a room, you have to build another room inside it and stop the sound from one room to the other".
The reason they saying that, is because the solid materials of one room cannot touch another room directly and if they do, the sound will transmit right through.
So when they do soundproofing, the so-called inner room is supported by clips they called RAIC "Resilient Sound Isolation Clips" or they also have something called Whisper clip and they line the walls with a sound absorbing material.
There is another way of doing this, but if you looking to soundproof something the system has to be designed, it has to be done the right way and this will cost a little.
Anything else, like filling joist cavities, with Roxul, foam, etc will only muffle the sound a little, the main sound will travel through floor joists. If it was so easy everyone would be doing this.
P.S Take living space above the garage, you have insulation in every bay, you have a double layer of 5/8" sheetrock, you have 3/4" plywood, you have padding and carpeting on top. When garage door opens, the sound is muffled a little, but you can still hear it in the room as you standing under garage door opener.
I hope that explains a little.
Q
Soundproofing
Q