You should plan on using AC power for all your equipment. Some small projectors (but few room-to-room portables) can run off of battery power, and some even claim to run for long enough to watch a movie. But they typically drop brightness significantly when using batteries, and most aren't bright enough for a backyard movie night at a suitably large size even using AC power. Beyond that, simply as a matter of convenience, the more individual battery-powered devices you're using, the more of a logistical chore it is to make sure each one is sufficiently charged before you start. For safety's sake, add a professionally installed outdoor outlet near the equipment location, so you don't have to use a trip-me-up extension cord or a chain of cords and power strips. And make sure any outlet you plug into includes ground fault protection to guard against electrical hazards.