You mentioned it has been painted. You want original, and would like something other than paint or polish. Here is why you don't want original, and paint is the best alternative;
First, you have to understand what the protective coating originally was. This was bare cast iron coated with stove polish. Buffed smooth and shiny. Then fired for final cure. Stove Black, or polish was used before high temperature paints were formulated. The coating is not impervious to water and water vapor like paint, so the metal will rust under and through the coating. Polish requires reapplication and sometimes abrasive to remove rust under coating that forms since when unused, water vapor in the air goes right through the polish. That is the problem with keeping it original. It comes with constant upkeep. Paint is far superior.
Paint when done correctly is the best protective coating, and does not crack, or peel off. It can be removed with paint remover if the original finish is desired. It does not decrease the value since it is there as a protective coating that can be removed. It is soft until fired for final cure. So you can spray multiple coats or wipe with mineral spirits until you get the finish you want before firing. You can't simply paint over cured polish. When heated for final cure, the pores in cast iron open and allow more polish under the paint out of the base metal. It is not easy removing original coats of polish. The best is having it sand or media blasted down to bare cast iron. Paint with a good high temp paint, and fire outside with a few pieces of stove pipe installed for final cure.
You're getting answers from pros that recondition and install stoves. When one comes along with polish and paint, I offer half the value since the time to remove all coating and paint, or blast and reapply polish back to original can be extensive. Reconditioning a stove with coats of polish is also double the cost of removing paint only. You can wipe old polish with lacquer thinner, wire wheel it, wipe again, torch the surface, try anything from naval jelly to lye. When you heat the stove and wipe with a damp rag, black will come off until it is blasted. You "can" get it good enough with a wire wheel and thinner, but blasting is days quicker.
Stove Bright Satin Black will give you the original look without the hassle of polish that will not protect the iron as well as impervious paint.
The top of the stove was treated differently. Lard was used the same as seasoning a cast iron pan. The lard or oil polymerizes with heat, or cross links becoming a different material capable of higher temps before burning off. Since a stove top goes over 500*f, this must be done constantly. Today pigs are fed differently, and the lard is not the same. Crisco works, as well as some oils with a high smoke point. If you use bacon grease when hot, and mind the stove top temp, it can last a long time. (I do bacon about 3 times and wipe a medium hot top which builds up a good seasoned coating if you keep top temps from smoking the coating off) There is an entire science behind it. But anything on a stove top needs maintenance. It must be heated with any oils since over time they go rancid and smell if not cured. If this will not be used, boiled linseed oil allowed to dry on the cold top will put a hard coating on it after drying a few days. I do the bottom of lids and inside firebox for a display stove to protect the iron from moisture and air. It's a durable almost clear coating. For display only, the top could be painted with the rest of the stove, but that is far from original. I would blast, paint, fire, and linseed oil the cold top. (Polish is not for the machined smooth surface or smooth steel plate, it is for rough cast iron only)
I collect this stuff, but use paint.
