Yeah, that is a Slim alright. They are fantastic razors. I prefer my Fatboys but just ever so slightly.
There is a date code on it if you want to find out what year it was produced. That razor will clean up quite nicely with some Scrubbing Bubbles, hot water, and an old toothbrush. Add a tiny amount of Flitz to a soft cloth and it should polish up good as new.
Those Gillettes were built to last forever.
If the numbers and dots on the adjuster need paint, you can use a black crayon and wipe off the excess. It works well and lasts.
Not sure what your blade of choice is but Feathers work well for me in the Slim. Don't be afraid to crank up the adjuster to a higher number. I stopped at 7 and I don't have that thick of a beard but it is wiry and a bit tough to mow down. I started out at 3 when I got a slim to replace the one I had as a younger man. Back then, 3 was the perfect setting.
I guess 20 years of aging has made the whiskers tougher. I got horrible shaves with the first slim and Fatboy I bought a few months ago...nowhere near as good as my E Jagger. I was about to give up hope until I cranked up the dial to 7. Eight brings out a weeper or two.....seven is perfect. Very close, very comfortable.
I'd love to see an "after" shot of that Slim with the original plating. If it were me, and you enjoy the way it looks and shaves, I'd get a second Slim and rhodium plate that one instead. The slims can be found everywhere.....and sometimes for very low cash.
Date code link.
http://gillettedatecodes.com/