I'm installing a new fiberglass tub and acrylic surround. Do I need to install greenboard from the ceiling to floor or can the tub and surround be installed with nothing behind it?

Most fiberglass units attach directly to the studs. The surround edges are designed so that your drywall will overlap the edge flange.

Some of the cheaper surround versions have a very thin surround material. This style is attached to some form of backing sheathing - greenboard, concrete backer etc.

In either case, the instructions with the unit or on-line instructions will tell you what to do.

Thanks for the info. The surround appears to be cheap because it does not have any flanges, so I'll have to use greenboard to glue it down. Since this is the case, would you recommend going ahead and using a 4x8 sheet of greenboard or should I only run the sheetrock down to the tub flange?

At a minimum, I would use greenboard in all areas behind the surround. Continue the greenboard past the edge of the surround for the full length of the greenboard, then change to regular drywall.

However, I would prefer to use Hardibacker as the backing material instead of greenboard. Hardi will not be affected by moisture while the greenboard can still be destroyed by a small leak over time. Greenboard is still drywall and can turn to mush if exposed to water. The only downsides to Hardi would be that it will take more mudding effort to make the exposed areas not covered by the surround as smooth as the remaining drywall and the fact that Hardi will cost about twice as much for the same area.

Consider loosely packing the voids of the underside of the tub with fiberglass batt insulation prior to seating the tub. It helps to muffle sounds and keeps the water a bit more insulated for those longer soaks.
I have heard it can be a good idea to fill the voids in the corner shelving with the expanding foam. (Make sure it is safe for the plastics) It helps make them feel and sound more solid and also a bit stronger.

I have seen the underside spray foamed as well.