Lizzie Lenard has a great method to clean up the needle bar and presser bar. Take an 18" thick cotton string, dab a bit of metal polish at the halfway point, thread one end around the bar, bring to front and cross the string ends. Pulling back and forth, moving it up and down, will get the bars cleans.
I would caution you not to remove too many parts. I took way too many parts off of a frozen Singer 128 laVendedora, then decided I probably wouldn't get it back together. Turns out oil, time, more oil, and possibly heat would have been enough to get it moving again. Still sad about that one.
Metal polish is also good for the face and inspection plates, even the Singer badge. Just be careful not to smear it on the decals or black finish.
And yes, I would leave that Revco reverser on. Its a bit of a process to install one, much less remove it and find the missing stitch length screw.