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Hard to find an image that is real close. but think cinema screen as large as we can fit on front wall, of course front speakers in wall. I do like the starry ceiling. These are NOT the colors. lol. This is somewhat in the ball park
So, when I look at this photo, I think that the use of very light fabrics in the room is a poor design choice. They have good edge lighting, but you can clearly see that the theater is dim. There's not a good way for people to read, or watch the game. You can NOT have any of those lights that are currently on, on when the projector is on. No lighting should be in a position to cast light directly onto the screen. So, sconces, for example, are completely stupid. They cast light in a place where it helps absolutely nobody, but it makes the on-screen image look worse. They are a beautiful design aesthetic, but not an actually practical device.
I love doing floor standing speakers behind a perforated screen. This means you go to Seymour AV. NOBODY ELSE! They have 4K rated perf screens which are excellent and well loved by those who have used them.
The UF material with a proper image size.
Your desire for a 2.35 scope screen is reasonable at your budget. I would strongly recommend getting a anamorphic lens plus a motorized sled. That's going to be the proper and best solution for your room. BUT! You will want to be sure that your room doesn't support the 16:9 screen height if you do this. There is no reason to spend the extra money on a anamorphic lens and to do a 2.35 setup if the room height is so tall that you can fit a 150" 16:9 screen in place instead of a 140" 2.35 screen. It not only costs a lot less, and is less complex to setup, it also will give you a sharper (slightly) overall image and will be consistently easier to use.
If you do have the height for a 16:9 screen, but really want to have it look like a 2.35 screen when watching 2.35 movies, then you can get a electric masking system. This is better, IMO, than using an anamorphic lens.
Be aware that you will want 10" to 12" of screen diagonal for each foot of viewing distance. This is why seating distance is the very first measurement of any home theater design. If you sit 12' away from a 92" screen, then any resolution beyond 1080p is useless.