I worked for a large building materials manufacturer for years, we provided acoustic solutions and designed acoustic materials, acoustic room solutions, we had a testing lab and even an anechoic chamber.
Don’t get too hung up on the 2X4, 2X6, 2X whatever.... Only consider that if you are trying to keep sound from entering adjacent rooms. If that is what you are after, I would build a staggered stud (look it up) wall, maybe even use a resilient channel or "hat" channel to isolate the drywall from the studs, calk around everything and fill the cavitity with fiberglas. You don’t need to use anything expensive, just use a plain fiberglas. R-11 ill work fine.
Sound is controlled by absorbing it (insulation), blocking it (that is why people use drywall and double layers of drywall) reflect it, (room dimensions, hard surfaces, diffusers).
The key is using a combination of these to achieve the desired results. In a large room the sound will reverberate and you will get unwanted "noise" created from it. that is when you want to use absorptive materials like curtains, carpet or even absorptive panels. Thicker acoustic wall panels will absorb lower frequencies better than thinner panels (think low frequency - large sound wave needs thicker material to absorb it) so size and thickness are important, you don’t want to just buy panels and hang them randomly, you could do more harm than good. A large room is ok if you can control the sound in the room. People use bass traps and diffusers to make the sound react differently in the room. Hardwood with rugs is a good idea because you can move rugs around and try different areas, types.
Also... spray foam is not a good "insulator" of sound it is much denser than a typical fiberglas batt and could actually reflect sound more than absorb it. Use a combination of methods and play with varying types. It may take a while but you can get a good result. (minus testing the room for reverberation and calculating the amount, type thickness of material you need, that can get pretty expensive).