I'd consider using cement board - cbu. Greenboard has a water repellant surface, but when you drive screws through it, it is nearly the same as drywall. For a vapor barrier, you can use either the roofing felt or plastic sheeting. Just staple it to the studs. Assuming the tub has a tiling flange or some sort of flange around the alcove sides, run the vapor barrier down over that flange on the inside of the tub and cut it off so it won't show prior to installing the sides.
The ceiling is not considered a wet area in a shower unless it is a steam shower. Greenboard is not required, and actually isn't as strong as plain drywall. If used, it should be strapped so it can be screwed in at 12" spacing, not the 16" in normal joists. If you prime and paint it well, and have ventilation in the bathroom, it will last as long as greenboard with fewer problems and isn't as likely to sag.