What type of drywall do I use around a zero clearance fireplace?
You can use whatever materials you would normally use.  A "zero clearance" fireplace means wood and other burnable materials can be safely adjacent and touching the fireplace.  The fireplace internally isolates the heat box from the casing with free flowing air to keep the outer casing cool.

If there was sheetrock there before and the rest of the room uses that, sheetrock is probably the simplest and least expensive.