Ken - make sure it isn't a pre '64 Winchester as the gun could be worth a fair amount of money depending on the caliber and model. It is worth looking into.
Because the gun has a crappy finish on it, doesn't mean it cannot be restored and still worth more than just being a shooter.
I used to have a buddy that was a gunsmith (bastard moved to Colorado so he could hunt more often) and he hated refinishing stocks, and I liked it. I helped when I could. He always removed the stock (or pieces) from the metal before starting. If you do this, make sure you are using hollow ground screwdrivers to make sure you don't strip the heads of the screws.
This is EXACTLY how we did it:
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only thing I would do different would be to sand the poly a bit to break the surface, and to help break up any lubricant that will be on the surface of the finish that would keep a chemical stripper from penetrating. Be careful with the chemical strippers as they may discolor or eat into the metal.
Tru Oil is easy to use and will put a beautiful finish on your gun. Just coat away with abandon, and after about 5-6 coats you will really have a good, durable finish. When the finish is about 30 days old, buff it out to the sheen you want, put on a couple of coats of good quality paste wax and it will stand all kinds of inclement weather and hand wear.
As far as touching up scratches wear, or use areas on the metal in which the bluing has come off, get the correct color of Birchwood Casey's bluing. I don't know if they still do, but they used to make a blue that would match rifles, and a blue/black that would come really close to matching the old S&W and Colt hot bath factory blue. Excellent products, and easy to apply.
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