24X40, reflective paint over drywall, budget as little as possible of course. This room already exists and is in use. I am currently using an older Sharp. Works well but a bit noisy and does not have modern inputs. I think it is a PG??X40 something, can't look at model right now sorry.
If your looking for 1080p and not 4K, Benq has a number of dlp projectors that are fairly bright. HT1070 refurbished can be had for under $500.
I use a Sony hw40 but have seen the Benq and it throws a great pic for the price.
If your wanting to go 4K on the cheap Epson and Optoma both can be had for under $2500.
The Epson uses pixel shifting to achieve an almost 4K image but does look great with 4K. The only problem I had with the Epson was the motion.
The motion on the Sony is tops in my opinion.