You're doing a video studio, not an audio studio, and video spaces tend to not have the walls actually in sight, but usually behind a perimiter cloth - often black heavy cloth, with maybe a coloured cloth on a separate track in front, or the wall behind painted. You'll have hard floors too of course, so what the space normally needs is absorbtion - lots of it. Loads of studios simply batten out the walls to allow rockwool between the verticals. Often theyre simply chicken wire covered and left (in quite a few big broadcast studios) or sometimes fabric covered to 'posh it up a bit' to be seen.

The usual recording studio aim of non-parallel surfaces doesn't really appear to often in video studios. The spaces are large enough to not have a characteristic 'sound' - mic to subject distances can go up compared to a room with reflections. Its actually amazing that two or three cloths, even light weight ones can really deaden a square, hard surfaced space. Mine is about 55ft in length with a low 9ft ceiling - not ideal but workable, with only 14-16ft width, and I have 25ft of it with a semi permanent standing set surrounded on 3 sides with cloth hung from my lighting grid. I'm very content with the sound - which is very controlled and neutral.

Agreed with Paul about the rectangle shape. Usually even studios with slanted walls are rectangular structures. The angles are created by the interior finish treatment, usually some sort of facade housing the acoustic treatment.

With regard to price. It's the cost of high end home construction, and usually 3x per square foot due to all the extra layers of material and labor. So 75-225$ per sqft is the range in general. 

If you diy it it can be done for 35$-50$ per sqft. This would be for the England Area, as costs vary by region.

Since the isolation is the the most expensive part, you want to carefully evaluate the noise levels that exist, and the noise levels your likely to create, as well as your local ordinances for noise. 

Knowing those three noise levels in decibels (A- Weighted) will allow you to determine what construction methods are required for your needs. You want to only build what you need, because again, isolation construction is a disproportionately expensive part of the studio.

A standard double wood frame assembly would be layers of exterior sheathing (OSB or plywood) which is your first M, then Airspace, then a internal franes covered with 5/8" fire code drywall in the room interior. Thats your other M.  Both walls should be insulated with the cheapest code compliant insulation, usually the pink fluffy stuff. And the walls should be air sealed.

I suggest you get Rod Gervias book, "home studio: build it like the pros". It focuses on music studios, but the principals are the same. It's got excellent drawings which you can give to your contractor and building code offices.

Since your new to studio design and construction I highly suggest you hire a pro designer to help, as typical building contractors won't know how to build studios, even if they think they do. Trust me, they don't.

Rod Gervias is actually located in Connecticut and is a world class designer. 

When at all possible use only standard building materials. Avoid "acoustic" branded products. They're just overpriced and often inadequate. Standard drywall, insulation, masonry, and lumber are what even the best studios use.

If your floating a floor, or using isolation brackets, those product might come from an acoustic brand. Beyond that all the stuff is available at your local building supply place.

Your methodology and cost will vary depending on if it's new construction or your retrofitting in an existing structure like a garage or basement or warehouse.

I just finished a job on a ‘video studio’. It has virtually no sound insulation from the outside world, and internally is massive, think aircraft hanger style big! It has a decay time from a clap of well over ten seconds and as every surface is hard, it’s horrrible. Luckily, I have finished my particular part of the job. As I was leaving, the USAF landed B52 bombers on the disused runway. The site had been sold off for redevelopment when they moved out a few years before, and lots of businesses operate there now. However, they maintained their ownership of the runways and aprons, just not the buildings. They’re now practicing touch and go landings most weeks, and the businesses can’t hear themselves think.

video studios don’t always need recording acoustics, in terms of what we normally want. Isolation and control. They want as much height as possible, so often the roof is single sheet, so even rain can be heard inside. First things for an acoustic video studio is the isolation. Then if money is left, treatment. If you look at the bigger audio studios they do tend to be parallel walled, but just have lots of treatment and diffusion. Abbey Road is a good example. It’s pretty square. As you get smaller, angles become more vital.