8ft is fine. At 9ft the other dimensions are exact or very close multiples of 9. It is best to avoid dimensions that are the same or multiples of each other. There are always room modes but they are much worse when dimensions are exact multiples. 8x16x24 for example, if you could make it 9 that would be better. In your case making it 9 would make it worse.
If you want to spend money the sky's the limit. If you want to save money for where it will really matter, the single most cost-effective thing you can do by far is use 5/8" instead of 1/2" sheetrock. This costs almost nothing more, but blocks sound an additional 16dB. Walls framed with different studs to inner and outer walls can get you down around -20dB.
You can go all-out and bring it down to recording studio levels. If you want to spend as much on this one room as the rest of your house. Or you can do the super effective but inexpensive. Highly recommend super cheap. Because what happens, there is a background level when you get quiet enough any tiny little thing you notice- and it doesn't blend into the background any more because there is no background any more. So it stands out. You would never notice the noise coming around the tiny little e gap under your solid core door until the weather-stripping leaves only that tiny little place for noise to come in.
You definitely want the solid core door. With weather-stripping. Either an exterior door, or an acoustic door which will be basically the same only maybe have the seal at the bottom which could be nice. Run one 20A line for the system. Run another for lights and spare outlets.
If you want to spend money the sky's the limit. If you want to save money for where it will really matter, the single most cost-effective thing you can do by far is use 5/8" instead of 1/2" sheetrock. This costs almost nothing more, but blocks sound an additional 16dB. Walls framed with different studs to inner and outer walls can get you down around -20dB.
You can go all-out and bring it down to recording studio levels. If you want to spend as much on this one room as the rest of your house. Or you can do the super effective but inexpensive. Highly recommend super cheap. Because what happens, there is a background level when you get quiet enough any tiny little thing you notice- and it doesn't blend into the background any more because there is no background any more. So it stands out. You would never notice the noise coming around the tiny little e gap under your solid core door until the weather-stripping leaves only that tiny little place for noise to come in.
You definitely want the solid core door. With weather-stripping. Either an exterior door, or an acoustic door which will be basically the same only maybe have the seal at the bottom which could be nice. Run one 20A line for the system. Run another for lights and spare outlets.