Any mustard will do it – whatever’s in the fridge. If you’re buying something new, my pick is for a Dijon or seeded.
You can make this up to a day ahead – just store the sliced apples in their acidulated water bath with a lid until serving time, and don’t dress until the very last minute.
You can finely slice by hand, using a food processor, a mandolin with julienne attachment, or even a julienne peeler. Cut the cabbage against the grain for the best shaped thin slices.