Those are the dimensions of my bedroom and I have a pj setup in there which I think works rather well. Since its not huge, you can have a smaller stereo setup that will rock that room. I have my projector on the 12ft wall about three feet from the corner, shining in the middle of the wall projecting on a 92 inch screen which I don't always use. I like to project right onto the wall, which gives me about 110 inch, which works great. I believe the standard for distance and screen size is 1.5 times the distance for 720p and 1.2 x distance for 1080p. So to calculate the distance would be 92 inch screen size x 1.2 = 110.4 divide by 12 inches = 9.2 feet back from screen. So you could do two rows of seating from the back of the wall one from 13 on a riser, then the other from 9, and you would have a good arrangement. I wouldn't buy screen until you know how big you want it, you may want 110, which to me is not objectionable even from 6 feet away. Each person has their own comfort level, but with two rows, people who don't want to be close can go to the back row.
Far as those calculators, they can be confusing, I just go by the SMPTE Society of Motion Picture and Television Engineers which have a standard for theater dark lumens at 16 lumens on screen, in such a theater, they recommend no less than 12 lumens and no more than 21. To calculate it it is lumens of projector divided by sq ft of the screen, so for 110 it is 4.5 ft tall by 8 ft wide = 36 sq ft. My projector is 1600 lumens/36= 44 Or you can calculate sq ft image area x foot lamberts to get lumens needed, so 36 x 16= 576 lumens. Keep in mind any ambient light will require more lumens, and projector bulbs do dim. I like to read reviews to see what the best color mode of a projector produces far as lumens. So with my Epson 6500, that 1600 lumens is only for its brightest mode, but its best mode I think was around 600. I can say even with lots of light coming through around the closed shades in the day, it still look pretty good.
There are lots of projectors to choose from, and it just depends on how you want to setup the projector. For me I needed lens shift which allows a me to put the projector in different areas of the room without changing the shape of the picture. if you are mounting to the ceiling, you may not need lens shift and can save some money. One DLP projector I read about throws a 100 inch from only five feet. I think it was an optoma gaming one. Most projectors should provide enough lumens where you won't have to worry. You don't need to cut a hole in your wall, if your mounting on the ceiling, then many options are available. It really depends on what you are looking for far as features, price range, and projector placement. Let us know and we can give you some suggestions.