Dedicated theater rooms are great fun to build! Man, I started mine out with a CRT projector and a laserdisc player back in the day, but it's seen a couple of upgrades since then.
I'm just going to go ahead and recommend the projector that I currently use: a JVC DLA-NX7. It replaced a ~2011 Epson 1080p LCD projector, and the difference is absolutely insane. As it's a native 4096x2160 unit (not a "faux-K" pixel shifter), it's fairly expensive, but nowhere near the $25K or so that JVC charges for their laser projectors.
So why am I so in love with this machine?
-Unlike consumer DLP projectors, there's no rainbow effect.
-JVC added Frame Adapt HDR in a recent firmware update, which basically lets the unit adjust the HDR tone mapping for every frame of video, instead of relying on static HDR metadata to "get it right" for the entire video file. It works surprisingly well, and is about as close to Dolby Vision as you can get from a projector.
-The NX7 is an LCoS based unit (JVC calls it D-ILA). Although it is a liquid crystal based device, the pixel response time of liquid crystal on silicon is much faster than that of a standard LCD. As a result, 3D movies show absolutely no cross-talk. In fact, this thing handles 3D as well as my Samsung F8500 plasma. It's far better than any LCD TV I've seen--most of which suffer from horrendous cross-talk.
-2D motion resolution is also superb, with no visible blurring of fast moving objects. I've always used ancient versions of 3DMark to judge a display's pixel response time, because I used to see these benchmarks on CRTs all the time back in the day. I know exactly how they should look. Even today's gaming grade LCDs don't quite match the motion resolution of a CRT running these old tests. But on the DLA-NX7? There's not a hint of motion blur. Again, the only other modern display that can really mimic a CRT in these old tests is my F8500 plasma.
-The contrast ratio is absolutely unbelievable. You may have noticed the grey pillar box bars in the picture above. That's actually from the ambient lighting, not the projector itself. Turn off all the lights, and it's almost like having a freakin 110" OLED on the wall.
-The color accuracy is absolutely unbelievable. Out of box color accuracy is nearly spot-on. With a bit of additional tweaking? Perfection. Here's how a 4k/60 video looks on a 1.2 gain 110" AT screen. Projection distance is 16 ft, and the projector is running in low lamp mode.
-The bulbs are very stable--they don't lose nearly as much brightness as my old Epson did once they age past the 2000 hr mark.
-It is very quiet. I always run the unit in low lamp mode, which is more than bright enough even for HDR. In this mode, I can barely hear the fans.