I'm not sure you actually want a transparent background, you probably want a black background. Here's why:
A black background will block most of the light from the projector, except where your ghost is located. This will help keep your environment dark, making the projected effect more realistic.
A light background will allow the light through, illuminating the area, which is probably not desirable.
A "transparent" background would indicate that you want to overlay the video on top of something else, allowing that background to be visible instead. You'd typically do in the video editor (or something like Adobe After Effects), but you wouldn't want to save it with a transparent background. Unless you were doing something really weird
Hope this helps.