How do I prepare my new bathtub alcove?
First of all, greenboard is no longer accepted as a suitable product for wet areas. It has been replaced with "purpleboard" or glass-backed products without paper for mold growth.

Consider doing to tub alcove in a cementicious board like Hardi500 or a fiber-glass backed gypsum like DensGuard.

Do not apply a vapor barrier behind these if you intend to seal them from the room side. This will promote the dreaded "moisture sandwich." where any moisture which does get through the first barrier cannot escape the second.

From recently doing a similar project I am a supporter of the Kerdi membrane. You set the wall boards and seam them as usual (any board will do, but I like mold-resistant and water-resistant board)... then you "shingle" on the kerdi membrane with thinset. 

EDIT: I changed where I said "blueboard" to "purpleboard" as some googling showed I was using the wrong slang....