I've used both paints and polish. Rutlands Polish is what I have used but I've heard that's not a good brand really . There is two other ones on here that folks use that are better . I prefer the polish to be honest because I think it's easy to apply every summer and leave it where it's at without mess or mask . Paint always peels or burns off at some point in time and it's not easy to just spot fix and so on . If you are restoring I think paint is a good option but after the paint starts to "flake out " I would continue with polish but as someone else pointed out most antique stoves have some sheet metal components to them . Polish doesn't work well on steel . It only really works on the cast iron . Something to keep in mind .
Try them both out on some parts and see what you like .