Something like a BenQ 3550 could shoot about 100" diag screen with 10' of clearance. I am assuming your shooting across the 10' width of the room and subtracting about 18" for the depth of the projector will give you about 8.5' lens to screen. All these DLP's are designed to be inverted/ceiling mounted at or slightly above the top of the screen so mounting in a wall unit may be a problem. As for a screen if you want it flat tab tensioned is the best option for a drop screen. Whats your viewing distance and what is the type of content do you primarily watch and/or gaming? Bluetooth is the worst possible solution for audio as lag causes lip sync issues with video.
"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