The final factor is your room. A high contrast gray screen will help reject side ambient light. Assuming you can deal with the narrower ideal seating area of a high contrast gray screen, it should be the choice for movie watchers. It may help with side ambient light, and will lower black levels, (and brightness), but you should have plenty of lumens.
I should mention other than movie viewing. While the HC3800 is very bright, in "best", it's not much brighter in brightest mode. Still, with over 1100 lumens it should still be a good combo with an HC gray, figuring that you won't want to be watching sports and most general HDTV and TV in a fully darkened room. If your intentional lighting is on the sides, the screen will help deal with that
All this is not to say that a good white surface screen shouldn't be considered, but, I favor helping the black levels out a bit, and also, since this is a fairly entry level priced projector, and a bright one, it should find itself in a lot of family rooms, bonus rooms and the like, where things aren't as well controlled as in a dedicated theater.
I've been able to watch movies on my high contrast gray Firehawk G3, filling all 128" diagonal of the screen, and the images was nice and bright. For my sports viewing, I would have liked more lumens for the ambient light levels I prefer, but I solved that by just reducing the image size to about 110" diagonal and that gave me a small extra boost in brightness that made it work for me. Yes, I could have filled the 128 inches, but preferred the extra brightness.