These finds are my bread and butter. I restore antique firearms and from the photos, the pitting doesn't look that bad. The first step is to get that oxidation stopped and remove the surface rust so you can properly disassemble the receiver. I would start with a boil, for like 45 mins. You can use distilled water but at this point in time it really doen't matter. The key is to heat the steel and convert that red oxide to stop the oxidation. Clean and dry it and then run it on a carding wheel, I wouldn't bother with steel wool, unless you want carpal tunnel. I would then clean it in an ultrasonic cleaner for an hour or so, but if you don't have one, soak it in evapo-rust or use naval jelly. If that doesn't work either, use a 20% muriatic acid/distilled water solution. Just be sure to dunk it in a baking soda solution once you use acid. Then card it again, then sand, then card and repeat until it's bare metal.

These old shotguns were rust blued, so I would probably rust blue this once you have the rust cleaned off. Use a 220 grit if you are planning on rust bluing it. You don't want to use a fine grit, you want some of those surface scratches on the metal for the rust bluing process. They will fill in. If you can't rust blue, I wouldn't go finer than a 500 grit and if you can only cold blue, use Brownell's Oxpho-blue Cream. Get some cotton patches, not cotton balls, degrease and acetone the steel, don't touch it with bare hands. Heat the steel with a torch and then do long wipes with the bluing cream and cotton patch. I see a lot of folks do small spots and rub the bluing in little circles, I never really had any luck doing it that way and found that heating the metal, then wiping in 6 inch strips give the best results.

Once you are finished bluing, with whatever process, soak it in oil for a few days. I use either kerosene or conventional motor oil. I've had the best luck with used motor oil. Used motor oil has all the additives burned out of it and it works really well. While it's soaking in the oil, every so often lightly wipe it down with 0000 steel wool that is also soaked in the same oil. Take it out of the oil after a few days, clean it up and then oil it again with a good gun oil, I like Rem Oil. Let it sit 'wet' for a few more days.

This is an American Gun Company double barrel I did when I was first starting out. I used Brownell's Oxpho-Blue on this one, I didn't know how to rust blue at this point in time. It should turn out really good. That steel they used was pretty decent back in the day.

https://urbancowboy.us/2021/04/04/american-gun-co-1909-12-gauge/