I rather like the rustic~rusty?~ look of it and it doesn't have to look lovely to do the job. A good brush down with a wire brush, rub in a little stove black on the side, oil on the top and you've got yourself a stove. Even the heat resistant paint tends to bake off after awhile, so I wouldn't worry too much about painting it. I'd clean it and oil it now so the oil has time to soak into the metal and cure out...you can help it do that by building little fires in it~not too hot~and letting the oil bake into the metal. Some of it will burn off and stink a bit but you'll soon have a more finished surface that is easier to clean, the more you oil and burn your stove.
Should be really pretty once you get that baked on patina going.