1) I would like to do this to reduce eye strain. Would this approach even help?
2) What projector do you recommend? I guess my budget is around $1K to $2K
I have a MBP m1.
Have you tried experimenting with different monitors already? Bigger, better brightness and contrast, high resolution, etc.?
I use a QHD ultrawide zoomed in for bigger text, coupled with continual adjustments to room/window lighting and monitor brightness as the day goes on so ambient light isn't too bright or dim. That seems to help. Nicer monitors have a built in lux sensor that can do the same thing.
I've tried working on a projector before and the 1080p ones were super ugly and pixelated for text. The 4k ones were very expensive back in the day. Refresh rates kinda suck too.
Long version: If you are into convex tinkering, then try ordering a USD 200.00 LED projector off of Amazon and see how you like it before investing in a more expensive one. The LED projectors have almost instant cooldown times unlike BenQ projectors with light bulbs. The only drawback seems to be, that the cheap LED projectors lack mounting holes -- contrary to the official documentation both on Amazon and the manual booklet with the projector. The price is below USD 200.00 for a reason. Both my LED projectors are still working. Never really felt the need to upgrade.
Didn't really need a projector screen. My first setup used white backwall for a cabinet. The second setup is simply projecting onto off-white wall paper. Please note, that it doesn't bother me, but your mileage may vary. Please, also note, that I use gnuscreen/rlwrap/sbcl/vim in MacOS's Terminal.app. At 80x24 characters on 1080p at 60Hz refresh rate, it fails to be a MacBook Pro M1 screen experience. My crude setup may be insufficient for graphical artistical work.
If you want to save your back from sitting down a lot, then you can point the projector at the ceiling. This permits switching between standing, sitting and looking up. Having even more variety may imply headstands. This is where the missing mounting holes are a bit of a buzzkill. But simple solutions exist, if you turn the projector's box into a stand with a box cutter. Protip: Keep the air vents clear.
My setup was so popular with family, that I passed my first projector and stand onto them. That is why I got a second setup. Both are still operational and highly appreciated. Haven't productized it yet. If someone is interested in that, then please feel free to reach out. Don't mind going into business.
Please, feel free to ask questions in case they arise.