Kinda depends on the style of the film you want to shoot it in, but since the room is so small, you might not need too wide or too long lenses. It would be best if you could take a bunch of lenses or a director's viewfinder into the room to see what you like. But generally I have a feeling that you'd chose lenses between 20mm and 50mm.
Why Ultra Primes? You'll be able to afford more lens sizes if you get super speeds instead.
I think Max is right about going with lengths between 20mm and 50mm, if you must have Ultra Primes, but you're going to have gaps in size, no matter which three you get, where you really wish you had more choices.
Brad's right, for the price of 3 Ultra Primes you should be able to get a full set of Superspeeds (18mm, 25mm, 35mm, 50mm, 65mm, 85mm). On the other hand shooting with a limited number of focal lengths can be an interesting creative challenge. There are many directors who reply on a limited number of lenses, some only on one (Ozu, Bresson for instance)
Since you are on a soundstage will you be able to fly out walls or any other trickery? If so you won't need to stay nearly as wide as you otherwise would. If this were the case I would want atleast 4 lenses, 12,24,50 and 85. The 12 is really only if you want a really wide shot, and if you want to go even wider you could go with the 10. If you can't fly out walls the 85 will probably be of limited use and you may even want to swap the 50 for the 40 and you definitely want something wider than the 24.
Of course the subject matter and visual style will dictate a lot of this. For one film you may want to stay with longer lenses and on another you may want that extreme wide fish eye shot.
Get a directors viewfinder or even a 35mm still camera and get in there and see what you like the look of.
Just finished shooting a short called 'PADDED CELL'. The set was just that! An 8' x 8' x 8' padded cell in a mental insitution. We had 3 ultra primes, 16mm, 32mm, and 85mm. Although it was a small room, and was a psychological thriller, so 16mm might be a bit wide for your project if it's a drama or something. The DoP likes his extreme closeups so the 85mm was handy. Some people prefer to use a limited number of lenses, as it might give the film a 'look'. I would stick to three ultra primes, even if you have the budget to shoot on a full set of superspeeds.
Some people prefer to use a limited number of lenses, as it might give the film a 'look'.
That's a good exercise to try as an experiment, and some people make that choice for a reason, but if that's not the style you've chosen, then not having all the lenses you'd like is a hindrance. Sure, some happy accidents may occur because you are forced to use a certain focal length, but most of the time it's an advantage to have more choices in my opinion.