Winchester 37, bad shape

Without photos, it's kind of hard to give advice on what needs to be done.
However, I think you can do it yourself if you have any experience with tools at all.

0000 Super-Fine Steel wool & oil is your friend on the metal.
0000 Super-Fine Steel wool & Lemon Oil, followed by past floor wax is your friend on the wood.

See this about that:
http://www.thehighroad.org/showpost.php?p=7826470&postcount=1

rc

Super-Fine steel wool will not take off the buling if used with oil.

However, the rust has already taken off the bluing under it.

At any rate, I suggest you do get the rust off & stopped and then see how it looks.

If it needs re-bluing, I'd suggest a profesional shop who can try to make it look like it did when Wionchester did it.

You might try Fords:
http://www.fordsguns.com/index2-2.htm

rc

I've done a lot of these types of gun, mostly because they were someone's Grandfather's and there is sentimental value. Before you remove any rust, and I stress, BEFORE, you can try boiling the barrel and/or action in distilled water. This turns the red rust,[ferrous oxide], to black,[ferro ferric oxide]. Then, when you remove the loose stuff, what's left underneath will be black. If the rust is too heavy, things will need to be re-struck and blued. In this case, I've found rust bluing to be the better option. It tends to hide more of the heavy pitting better than a hot tank job. If you don't have anything long enough to immerse the entire barrel, sometimes a tall stock pot will do half at a time. This works well. Boil for 5-10 minutes. If you can't do that, you cover the freight and I'll try the boil and card method for you at no cost. Mainly because I've got a soft spot for family guns and I'm usually boiling something anyway. I'm in the south central Indiana area, so freight won't add up to much.
Luck,
Jim