The two projectors I would be looking at are the BenQ 2050a and the Epson 3100/3700. The Epson's are on closeout right now and an absolute bargain. Forget 4K you would just be wasting your $. I am assuming that this is a room with white ceiling and light colored walls so don't waste your money on a high contrast projector like the 5050. The Epson 3000 series has great brightness and great placement flexibility with lot of lens shift/zoom range where the BenQ is a little sharper and has great motion handling but very limited placement flexibility. Tab tensioned screen if you can afford it but a cheaper screen will work fine just don't expect it to remain perfectly flat, a condition some can tolerate more then others.
"Smart enough to know better, to old to care" ------ Dedicated Bat Cave Home Theater, JVC RS49U/Mitsubishi HC7900DW Projector, 110" 16:9 Jamestown screen with variable power masking for CIW 2.50:1 to 16:9, Marantz 7009 with 7.1.4 Atmos with Ohm mains,3 DIY Subs (2 15" (1 ported, 1 sealed and a 12" 4th order bandpass), 1 DIY butt kicker, Custom Built HTPC, 18TB DroboFS NAS