There will be no non-artificial lighting in the room. I have already taken out all windows in the room. So a white screen will be ok with me.
There's more to it than that though. For best front projector performance, light reflection needs to be kept as low as possible. Light from the projector will be reflected from the screen to the walls, floor and ceiling. The brighter those reflections are, the lower your contrast and the more washed out the colours will be.
Painting everything flat black would be best, but of course, few people want a room like that - including me. So, you need to choose your colours wisely and go with the darkest and flattest you can live with.
Then, there's lighting. Try to set up dimmable light "zones" on separate circuits. Sometimes you might need a bit of light in the room while the projector is in use. If you have a zone at the back of the room, you could have those lights on, while those near the screen remain off.
I have a DIY screen that I bought from Seymour and I'm very happy with the quality of the screen material. I built the wood frame myself, which was pretty simple to do. You can save a LOT of money by building a screen yourself. Or, if you aren't keen on doing that, asking a friend do it would be a pretty small imposition.
Having said all that, I would be loath to hide those CBT36's behind an AT screen and false wall. I think they look tres cool and I'd want them seen. But, if performance is your highest priority and you don't care if they are seen, than 3 of those across the front behind an AT screen and false wall would sound awesome, I'm sure.
If you do go that route, do your research - rework is a b*tch.
The "Projectors & Screens" forum has lots of info. BMXTRIX is the guy who can probably provide the most/best advice. Jostenmeat is also very helpful, although I haven't seen him posting lately.