Bob,
If you install a GFCI in a plastic box, the ground conductor will terminate to the receptacle. The plastic box does not need to be grounded. A metal box would need to be grounded either by attachment to a grounded receptacle or direct connection to the grounding conductor. The acceptability of the grounding of the box by the receptacle can be iffy, but don't worry if you use a plastic box.
Removing the old box without tearing up sheetrock may be difficult. If you are careful you may be able to use a mid size or jumbo plate instead of having to patch sheetrock.
Have you seen the old-work boxes with the ears that flip out to secure the box to the sheetrock? They are really handy, are larger than standard metal boxes, and sometimes the damaged area of the original sheetrock hole needs to be removed anyway for the larger box. Lowes and Home Depot sells them.
Before you start to remove anything in the old installation make sure you know what is involved in removing the old box. Some have two nails going all the way through the box and can be removed by cutting the nails inside the box with a pair of diagonal cutting pliers(dikes). If there is a bracket that is on the outside of the box you may need to tear up sheet rock to get to the nails or screws or with care you can push a screwdriver or heavy scraper between the bracket and wall to break the head off or pull out the nail or screw.
