Hi Stitchnripper, here's my 1918 Red-eye that was in similar condition as yours. It got a sewing machine oil bath, inside and out, and it was very gratifying to notice how it slowly eased itself back into a functioning machine. Our first serious rescue. Still needs work on the wood, someone smeared it heavily with varnish and now the wood looks like plastic.
I used 'Neverdull' on the chrome parts, basically cotton wool soaked in a cleaner/polish inside a can. The handwheel was as dull and black as yours, as were most other chrome parts, and a little elbow grease polished it right up. The other parts were a bit more challenging because they are more "fiddley" and I wasn't quite as ambitious with them.
I am not worried about some spots I didn't get all bright and shiny, like the bobbin winder - after all, it IS and old machine. This one may have been idle for a long time - it doesn't show much wear.
I actually really like the ones that show their scars - I am considering 2 very old ones that are not 'pretty' but have a lot of character :-) .
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