So the only points I was going to add or reinforce to what has already been said:
With basements, you have to be careful that you don't block air flow, because humidity tends to accumulate in the basement, and you don't want to set up a mildewy environment.
Which is actually contradictory to everything else you want to do, which is make as complete a sound seal between the two floors as possible. Doors are a big deal in studios, but pretty much every hole is going to be a source of sound leakage. So you kind of have to mitigate one against the other. When I was planning on building a small home studio in the basement of my former landlord's house, I was thinking of devising a system of letting the room breathe when I wasn't using it, and sealing it up when I was.
The duct work is a good point -- it's just like a car, you have to cancel both sources of noise and rattle, but it's also a conduit for sound leakage.