Hi there Lester, and welcome!
The room will be decoupled, (genie clips, hat channel, 2 layers of drywall, green glue between layers, ceiling also drywall on clips+channels)
Great! So clearly, good isolation is a priority for you.
The room's interior measurements are going to be: 6'6" x 5" x 6'1" (height)
Ouch! Not very big, and the ceiling is VERY low.

Have you considered ways to get more ceiling height? There's not even enough room there to put the acoustic treatment you'll need up there. I'd guess at least 4" of 703, or something like that. I hope you aren't very tall!!! And with such a low ceiling, you won't be able to get good acoustics in there anyway. I'd really try to rethink this, and figure out how to get the ceiling as high as possible.
The ventilation will run not outside, but from and into the rest of the unoccupied and sizable basement.
That might not be legal. Some building codes do not allow one room to exhaust air into another room. Better check that with your building code.
I will only run the ventilation between takes, so I am not overly concerned about it being silent. Reasonably quiet when it is running will do fine.
That's not a good idea, even though it sounds like it: you should have a constant flow of air in a studio, and especially in such a tiny space: There's only a few minutes worth of air in there: it will get warm and stuffy and unpleasant very fast, the O2 levels will drop and the CO2 levels will rise. Not a good environment for doing a good job! Better to build a system that can be on all the time, providing a stead flow of air.
I am, however, very concerned about exterior sound coming in through any holes, vents, ducts, whathaveyou even when the system is not on.
Even more reason to leave the fan on all the time! If the ducting is correctly designed and correctly isolated, then the fan will not be audible at all, and neither will the air flow.
I am taking great pains to float the room
Did you say "float" the room?

How are you planning to do that? Are you aware of the issues with trying to float a room correctly? You should probably read this thread:
http://www.johnlsayers.com/phpBB2/viewt ... f=2&t=8173
it seems most builds are concerned with recording while running their HVAC system. I'm not.
Yes you are, if you are smart!
With that in mind, should I still plan to build a box to baffle the sound like this
Most definitely! Absolutely! And certainly! The simple fact of having a hole through the wall or the ventilation duct destroys the isolation system, regardless of whether or not the fan is on. Building a proper silencer box restores that broken isolation, also regardless of whether or not the fan is on. So you need that anyway.
Here are some examples of how people have built their silencer boxes:
http://www.johnlsayers.com/phpBB2/viewt ... 0&start=45
http://www.johnlsayers.com/phpBB2/viewt ... 9&start=74
http://www.johnlsayers.com/phpBB2/viewt ... 25&start=2
http://www.johnlsayers.com/phpBB2/viewt ... 42&start=5
http://www.johnlsayers.com/phpBB2/viewt ... 61&start=0
http://www.johnlsayers.com/phpBB2/viewt ... 5&start=98
http://www.johnlsayers.com/phpBB2/viewt ... &start=157
http://www.johnlsayers.com/phpBB2/viewt ... =2&t=13821
http://www.johnlsayers.com/phpBB2/viewt ... 8&start=44
http://www.johnlsayers.com/phpBB2/viewt ... 2&start=16
Those are mostly bigger than what you will need, but the principle is the same.
Or is there a simpler solution that will serve my purposes just fine?
Nope. That's about as simple as it gets.
I wonder whether building an elaborate box to reduce fan noise that I am not really worried about is entirely necessary.
You seem to have the wrong impression about the purpose of the silencer box: it is not there to stop the fan noise getting in. It is there to stop ALL noise getting in, and also getting out. It restores the isolation that you broke by making a hole in the wall for the ventilation duct, so it blocks all noise transmission: The fact that it also blocks the sound of the fan is just a bonus, but that is not the main function.
so there are no worries at all about preventing sound inside the room from getting out, and plenty of worries the other way around.
It's a two.way street: if sound can get out, then it can also get in.
The two wall frames that are not up against the foundation walls will have a drywall layer on the outside as well, the two that are up against the foundation walls will not (don't want to make the 3 leaf mistake!)
How will you connect the "outer leaf" on those two walls to the foundation walls, while still avoiding flanking?
Ceiling has 24" joists stuffed with a double layer of Roxul,
24" joists???

Are you SURE that's what you wanted to say? I've seen some pretty big joists in my time, but twenty four inch joists are rather unusual, especially on a span of only 5 feet!
I will hang a 5/8" drywall ceiling on genie clip/hat channels as with the walls
so the ceiling will also be two layers of 5/8" plus green glue? Also, if this is a basement, then I assume there's a floor right above the booth: Why not use that as the outer-leaf, and put the clips/channel/drywall on that? Gain yourself several inches of headroom like that, which you will need for the acoustic treatment...
Floor will be Rug on plywood on Barrymat on crappy particleboard subfloor.
Why? This is a basement, so I'm assuming that there is a concrete floor down there: why add that unnecessary thickness of all those layers, when the concrete will do just fine as it is? You are wasting headroom like that, and you have previous little to waste!
I will probably be making corner bass traps out of the leftover Roxul (floor-to-ceiling), and will be buying some Auralex foam for interior treatment. (hoping that this will be sufficient for my needs)
Save your money, and just buy plain old OC-703 for the treatment.
Is building an elaborate box to reduce fan noise that I am not really worried about entirely necessary for my space and needs?
Yes, totally.
Since I'm not running a high volume air exchange system, what is the smallest vent hole size I can get away with?
You need to calculate that, not guess it. It's a rather complex procedure, but since you life depends on getting it right (very literally: you wont stay alive too long of you don't pump in enough oxygen!), it is well worthwhile going through it!
First, you need to figure out how many room changes per hour you need, based on occupancy and exertion. I'd guess maybe 6 or 8 for something like that. Now multiply that by the volume of the room, to find out how many cubic feet per hour of air you have to move. Now dived that by sixty to get the number of cubic feet per minute that you need to move. Now figure out the duct size that will allow you to move that amount of air at a speed of no grater than about 200 feet per second (it's a vocal booth, so the speed has to be even lower than for a typical live room): Now allow for reduction in duct size around corners, as well as the thickness of duct liner, etc. That gives you the final inside diameter or area of the duct. The outside diameter will be greater.
Now go back to step 3, where you figured out how many CFM you need (Cubic Feet per Minute). You need a fan that can move much MORE than that, because the amount that the fan will actually move depends on the static pressure of your duct system, so you have to figure that out. There are tables and equations to help you do that. For example, let's say that you need to move 100 CFM. You can't just buy any old fan that says its capacity is 100 CFM, because that rating is only true for free air (no duct) as soon as you put that fan on the end of a duct, it now has to fight the "resistance" of the air moving along all that duct, so it can no longer provide its full rated capacity. A fan rated at 100 CFM might only be able to do 60 or 70 CFM if the static pressure is high. So you need to know the static pressure, and choose a fan that can supply the right amount of air (CFM) when it has to work against that amount of static pressure.
It's a bit more complicated than just punching a hole in the wall and sticking a fan in it!
Also, I'd connect the fan to a door-operated switch, so that the fan comes on automatically whenever the door is closed, and turns off when it is open. You always want the fan running when the door is closed, even if you are not in there, to keep the temperature and humidity constant. (Ever smelled the inside of a fridge, closet, car or other small space that has been left closed up for a few days without air?) If you don't want the fan to run, just open the door.
What is the optimal material for the duct? PVC pipe ok, or... ?
Nope, PVC pipe is not OK. Metal round duct is OK. Sold very cheap in Home Depot and any HVAC supply store. The silencer boxes can be made of plywood, and lined with 1" duct liner. The final interior cross section of the silencer box should be at least twice the cross section of the duct itself.
What is the best way for me to get a small amount of airflow into and out of my room if my primary concern is to maintain the integrity of all the nice decoupling that I am trying to achieve?
With a properly designed duct system that includes a single fan, silencer boxes, and ducts that have been dimensioned correctly to do the job right.
- Stuart -