There is no issue with putting a screen in front of a window. As far as what projector/screen combo will work best we need a lot more information about the room. UST/ALR is best if you have a lot of ambient light but are the most expensive. Standard FP w/ALR as long as the ambient light is not from the same direction as the projector can produce a better image for a lot less money. Standard FP in a dedicated fully light controlled room with a standard screen is leaps and bounds better and will cost a lot less.
"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