That's fairly heavily rusted, but the first question I'd have is have you checked the state of the chimney, since presumably you are thinking of using the stove, and that's step zero for using it, new homeowners.
You can either give up and apply stove black (aka stove polish) to make it black, but still kinda lumpy with rust, or you can take more serious steps to remove the rust. The rust does not appear to have gotten to a point where it should impact the safety of the stove, so ignoring it and/or blacking it is a perfectly reasonable option. Firing the stove (after checking the chimney, please) will also make it easier to mechanically remove after it's been thoroughly heated for a few hours and allowed to cool down again.
Given that the worst of it is on the lid/griddle, go ahead and take that outside for further work on it, it should be easily removable, often simply by opening and lifting.
Personally, I'd drop the griddle into a container of water+sodium carbonate and attach a battery charger or other low-voltage DC source to remove the rust by electrolysis, or water + citric acid and no battery charger needed. Phosphoric acid also works, but costs more. Electrolysis has the advantage of not causing any additional damage other than removing the rust (it can't be overdone) while the acids can start eating good metal if you don't pull the thing out once the rust is gone.
For electrolysis, you attach some scrap iron to the + terminal, the thing you are de-rusting to the - terminal, submerge both (not touching each other) in the sodium carbonate (washing soda) + water electrolyte solution, and the rust is removed without further effort. An old phone charger will do it slowly, a large battery charger will do it faster. Do this outside, or in a well-ventilated (like, with windows and or doors open) garage, please.
You could also use an angle grinder with a suitable wire brush, but it's a messy process as you have already seen with hand wire brushing. Given it's a flat surface, sanding will also work.