"Regular" good-quality sewing machine oil is clear. It's a first choice to clean the finish, and to remove gunk. It is the most gentle cleaner, so try it before anything else. You can also use it to oil the machine once you're done with the cleaning, but tri-flow is better. About the yellow oil, I'm not sure what that is -- maybe synthetic? Possibly dyed so that you can tell the difference? I would ask that guy. Or maybe someone here knows?
I'm really curious (or nosy) -- where was the bobbin case??
The job is not hard, but set aside some time and just try to remove as much gunk from the machine as possible. About cleaning the paint and polishing the metal -- these things are cosmetic and don't affect the running of the machine, so I like to do them last. Be careful not to use alcohol on the paint because it dissolves the clear coat. The clear coat protects the remaining decals. So far I've only used oil on the paint. I've seen some people use castile soap or dishwashing liquid on decals, while others say water-based cleaners are bad. It's very confusing. One thing everyone agrees on is that you should test a cleaner in an inconspicuous spot first. But since the FW doesn't have showy decals, maybe oil will work just fine. It is the safest thing. Use soft cotton rags or cotton balls for cleaning the paint. Microfiber rags are not good because they are somewhat abrasive.
One last thing -- be careful not to get oil on the wires. Rain has a good tutorial for oiling the FW, but he missed one spot on the underside, on the left. Actually he probably didn't miss it in real life, but it's hiding from the camera. Put a small drop of oil in each spot where metal rubs against metal. Turn the hand wheel and look for these spots. You can do it without the tutorial, but the tutorial is nice, especially for the warning about the spots near the wires. For lubing the gears you can use Singer lube, petroleum jelly, or tri-flow lube.
Rain's oiling tutorial:
http://vssmb.blogspot.com/2011/07/ho...sing.html#more
Rain also has a favorite metal polish --- I forget what it is, but you can search his blog.
I think your mom's machine is in great shape considering that she made all your clothes. (Pics are in another thread.) The FW was also our family machine. My mom didn't make many garments on it, but she did make me a beautiful fancy dress when I was 13. She used it mainly for altering and mending, and I learned to sew on it and made a bunch of things. When I was a teenager I abused it by sewing denim and leather. It is not nearly in as nice shape as yours. Your mom took good care of it!