You are talking about stopping penetration of sound. I've researched the question some. You would be best to hire a builder that specializes in soundproofing. I know from my own doityourself projects that normal contractors know very little about the subject. They tend to consider the fine and very important details a joke. Just like insulation company inspectors find that almost all contractors install fiberglass batts wrong because they laugh at the importance of the fine details.
Here is a brief of the building products issues:
To start with, HVAC ductwork is your biggest problem. Professional studios and conference typically filter the air through a big device that I can't remember the name of. For a 8 inch duct it is about the size of a small refrigerator starting at 200 dollars. It traps sound by creating turbulence and running sound waves into sets of flexible metal so there is no direct path through the device for sound to move. By the time sound reaches the other side it is less recognizable.
Insulating wall or ceiling voids. Any insulation will help suppress middle and upper range frequencies. Bass isn't bothered. There are three that stand out: Closed Cell spray foam, Wet cellulose installation and Mineral insulation batts. Wet Cellulose installation will fill and seal the void it is sprayed into and is fairly sound resistant. It is the least expensive of the three. Closed cell spray foam is a hard and heavier spray foam insulation but is expensive and a touch less resistant that cellulose to sound. Mineral insulation batts are the heaviest insulation, most sound resistant due to its weight. And it is completely fireproof, which is its primary application. No matter what you use follow normal install instructions. Compressing insulation isn't a good idea.
Framing: The best is a double wall. This means different sets of studs touching each side. The farther you pull them apart, the more sound resistant the wall will be. Sound travels poorly through air or correctly installed insulation. In a ceiling it is best to have a separate set of joists of the upper floor and ceiling directly below. Ceiling cavities are generally bigger than wall cavities which gives them an advantage.
The second best is metal resilient channels suspended by sound clips on existing studs or ceiling joists. When hanging drywall on them make absolutely certain that fasteners(screws, nails) never touch the studs that the channels are mounted on. Good luck getting a drywaller to do that.
Finishing layers: The goal is to add mass that sound has to penetrate. The more mass, the more sound resistance. In a wall it should be installed so there is a room, layers of drywall, a cavity, layers of drywall, then another room. This is a two leaf install. Don't install additional layers of drywall somewhere in the cavity, that will weaken the sound resistance. Stack all drywall layers on one side or the other. Depending on the wall a 1/2inch of drywall on each side will stop 30 to 55 decibels of sound in the mid range of audible sound. It depends on how well sealed the wall is. Doubling the mass of drywall will increase sound resistance by 8ish decibels in that range each time you double it.
Seal the wall: The outer most layer of drywall on each side of a wall has to be sealed with a flexible sealant. All edges need to be covered. Drywall compound will not seal the wall, the stuff has huge amounts of cracks that sound exploits. Just because you can't see them, doesn't mean they aren't there.
Other products:
Sound resistant treatments: Gels are naturally sound resistant. When they vibrate, the gel converts the movement to heat reducing the vibration. Therefore sound resistant treatments for drywall will reduce the energy of a sound wave quickly. Companies have developed gel like polymer compounds that never harden for this purpose.
Mass loaded vinyl: This is the building product with the most mass. It is a sheet of vinyl with embedded bits of very heavy metals. It makes a fine under layer for finishing.
Homasote: fiber based product that is the traditional soundproofing solution. Not a bad product, but too lightly weight to resist low frequencies as well as other methods.