The BD screen is very nice, but is completely pointless in a dedicated space. A good projector with a well built screen delivers an extremely high level of quality for a good price. The BD screens are very nice, but tend to suck up light which reduces the punchiness of an image, and while it maintains great contrast, it only needs to if the room was poorly designed. Basically, it's a very good Band-Aid to a poor room design. (I have a love/hate mentality with the screen)
If you are properly designing your theater space, then that means you intend to put in dark carpet, paint the walls dark, and paint the ceiling dark. No white trim, no white anything if you can avoid it. Use flat paint.
For lighting, you want no less than 2-zones of recessed, directional lighting, and possibly many more zones than that. Lighting is very typically, poorly implemented, so plan accordingly, attach photos/drawings, and ask questions before you wire the lighting in. I swear, no electrician seems to have a clue how to properly light a theater.
I think your budget is high.
That is, a mid-level projector like the RS46 from JVC will give you 95%+ of the performance of any projector you can get under $10,000. Mostly due to the incredible black levels it delivers.
For a great screen, I would look at the DaLite JKP Affinity screen. It is designed from the ground up to pair with high resolution home theater projectors with a perfectly neutral tone to not shift the color spectrum or alter contrast ratios significantly.