Hi Mike, and Welcome!
Here's something that might interest you:
http://www.johnlsayers.com/phpBB2/viewt ... =1&t=14147
I won't need a booth floor and I would just put the walls directly on the carpet.
Correct: You won't need a floor, if you build it correctly.
However, setting it on carpet is out. Carpet will not provide the air-tight seal that you need, since it is porous. In order to obtain isolation, you need the best possible seal you can, and carpet is not it. So either you'll have to cut out a patch of carpet where the booth will go, or you will have to lay a sheet of plywood on top of the carpet, and build your booth on that.
Carpet is bad for another reason: Lousy acoustics! If you really want your booth to sound bad, then put carpet on the floor. And if you want to make sound even worse, then carpet the walls and ceiling too...
And apart from anything else, you'd wreck your carpet anyway by standing all that huge amount of mass on it...
Major concern is noise isolation from outside the booth
You should try to put a number to that, in terms of how many decibels of isolation you want. What once person considers "good isolation", then next guy might say is "really lousy isolation", while a third guy might call it "extreme overkill". Numbers clarify that.
and not a dead sounding booth.
Well, on that point, you lose. There's no choice here, since you say that it has to be very small (just 4x5x7), so there's no other option, acoustically. You can make it sound dead, or you can just leave it sounding terrible. For such a tiny space, those are your only two choices. In fact, even when treated to be "dead" it will still sound somewhat "boxy", and "closet-like". It's just the nature of the laws of physics, applied to sound waves in very small spaces. Very small spaces cannot sound good. Sound waves need large spaces if you want them to sound good.
I haven't figured out the ceiling yet.
Same as the walls. The door also needs to be built the same way, and so do your ventilation silencer boxes, and the window (if you have one), and the electrical and signal pass-throughs.
My thinking at the moment is 2x4 walls with two layers of sheet rock
Two layers of drywall as a single leaf will give you about 30 dB of isolation between you and the room around the booth. Obviously, that will be higher with respect to levels in other rooms, at other points in the house, and also with respect to the world outside your house. But you still need to figure out if that is enough, or not Loudest human singing can put out an SPL of about 90 - 100 dBC. 30 dB of isolation would bring that down to around 60 - 70 outside the booth, which is about the same level as normal to loud conversation. If you only sing softly (romantic ballads, for example) then that would be more like 70 - 80 dBC inside, meaning 40 to 50 dBC outside.
I have spent hours and hours researching and as you know, it's like trying to drink water out of a fire hose.
Yup! And if you have only spent "hours" on it, then you've really just been taking a few tiny drops from the fire hose... I don't mean that facetiously, but seriously: acoustics is a huge subject, and just a few hours of investigation won't get you very far. Just scratching the surface.
or putting another piece of sheet rock on the inside (maybe using a channel?).
That would increase your isolation yes, provided that you used proper resilient channel (RC-1), and not just ordinary hat channel, which looks very similar but is totally different acoustically. Or you could use hat channel provided that you mount it on RSIC clips, or some other type of good acoustic resilient clip. However, doing that would eat up a lot of space, as you'd then have to put your acoustic treatment on top of that inner leaf of drywall, but you don't have any space to waste! You'd lose a minimum of 8 inches in width, 8 inches in length, and 4 inches in height. Probably more...
So you could go that route if you need more isolation that a single leaf can provide, but you'd need to expand the footprint to compensate for the lost space. In fact, I'd expand the footprint anyway, as large as possible, to reduce the typical tiny-room "boxy" sound.
Cost? As low as I can keep it.
Wouldn't that be nice! But in the world of acoustics, "low cost" is not part of the vocabulary...
So to recap:
1. Built on concrete with carpet and pad
2. 4x5x7 vocal booth
3. High sound isolation,
4. Not a dead booth
5. In-home daycare
6. Proper technique for walls
7. Low cost.
That's a great list, by the way! Pick any two items from it: you can have those, but not the others. Which two would you like?
Is it okay to build directly on carpet?
Nope.
Suggestion on ceiling
Same as walls: 2x4 joists, with two layers of 5/8" fire-rated drywall on top, thick insulation in the joist, fabric cover.
Whew! That took longer than I planned.
Yup! Welcome to the world of acoustic design! That will be your reality from now on: EVERYTHING will take much longer than you planned, and will cost a whole lot more than you planned... It goes with the territory...
- Stuart -
so he isn't doing much yard work. Two houses away, more of an issue. I do get a fair amount of traffic along the opposite side of my house. I chose this room because it is away from the AC outside and the furthest point from the laundry room. 
