I use the same projector I use inside. I think it's this one:
epsonFor the screen, I have an old pull down one I picked up from a school auction years ago. I just hang it from my pergola.
For sound, I already have a pair of yamaha outdoor speakers mounted for music. I hook the projector up to a FM transmitter and send the sound inside and then back out through the speakers. Not a great sound setup, but it doesn't require hooking anything extra up, so it's a winner.
I also have a portable bluetooth speaker that has an FM tuner, so I can move that around the yard as needed.
I've been surprised at how well it works. As long as the movie isn't really dark, we can usually start them at 8pm. I also invite my neighbors over if we're planning to be out there late to minimize complaints.
Edit: Also, a 100" screen inside is HUGE. a 100" screen outside is meh. Photo shows projector before being strapped down so that it wouldn't fall into the water.