You should start with a good primer on the drywall and then use a water based exterior grade paint.  Oil or solvent based paints can leave a lingering odor in the wine cellar, if you don’t have time to let the space air out.  Make sure your painter covers the drywall all the way to the floor.  Typically they will stop an inch or two short of the floor as they know that will be covered with base molding.  Your molding will be on the front of the racks, so this can leave an unsightly gap showing if they do not run the paint all the way to the bottom.