You are right, there are a lot of differing opinions here since everyone has their own experiences and preferences. In the end, what YOU consider the "best" screen will come down to personal preference as well, all we can do is share our experiences with you.
Here is my $0.02.
If you insist on having such a large screen you're not going to be able to go with a gray screen unless it is a very
light gray, and my guess is that you would be best off with a white screen. This means for best image quality your theater should be as dark as possible when viewing. The darker the walls, floor and ceiling the better; the less light hitting the screen (expect the primary PJ beam) the better. The main problem with a white screen is that it doesn't take much secondary (or ambient) light striking the screen to make the image lose contrast.
Using the PJCentral calculator I'm only getting 8 foot lambert of illumination at the screen with your PJ and screen size; movie theaters try to get at least 16 fL. so even with a new lamp you are already at half the image brightness of a commercial theater and that lamp will dim with age.
No matter what paint or paint mix you end up going with you should prime your wall. Kilz2
is a favored primer, but for a few dollars more you can get Kilz Premium
which is a brighter white. A wall painted with Kilz Premium will look almost as bright as one painted with one of the ultra white paints from Behr or Valspar.
The idea is to prime the wall/screen and then calibrate your PJ to it and watch some movies/TV on it for a while and note what you like and dislike about the quality of the projected image. Are the colors saturated enough? Are the black areas of the image black or just a dark gray?
After you know how a white screen performs for you, you are in a better position to know where to go from there; and so are those giving you advice.