Need some recommendations

Got a new place with a living room that that really leaves nowhere un-awkward for the tv to be set up, yet is primed for a projector setup. That said:

1) Budget: no more than $700 (only going that high if it’s a necessity).

2) 115” screen (diagonally (100”x56.25”)

3) About 15’ feet back from the screen

4) About 15-20’ from the couch to the screen

5) Ceiling mounted.

6) For movies/shows/YouTube

7) Living room

8) Both ambient light and no light (have five windows in the living room, but will use blackout curtains as needed/desired)

9) White walls/ceilings; carpet floors

I’d prefer refurbished/used.

Let me know if I’ve missed any necessary specs. Otherwise, please let me know what, if anything, I can get with these parameters. Thank you!