The black one looks like is has old dirt/oil "grunge" so it will need a good "cleaning" before you can do the "shining".
Some folks use sewing machine oil and either cotton balls, or soft cotton cloth (old t-shirts) to clean the machines.
Some use a mild soap and SPARINGLY wipe small areas - again with a cotton balls or soft cotton cloth. Make sure you rinse (againg sparingly) with clean water and DRY the machine.
I use a combination of both. If I strip the machine down I'll take some of the parts into the kitchen and wash them with soap and water, rinse and dry. For the head itself and any part that I don't remove from the machine - I prefer to use sewing machine oil as I don't have to worry about a water issue.
If you used the machine oil method, wipe all surfaces well with a clean, dry soft cotton cloth to remove as much excess oil as possible.
Once clean, dry and free of excess oil ... you can use a good quality carnuba wax on the painted surfaces of the machine to give it a nice shine. Just follow the directions on the can.
I use an oil based metal polish/cleaner (can't remember name and I'm not at home) for the chrome/metal parts. I generally do not wax these parts.
As for the wood case I can't help you. The FW cases have a covering on them, and not having a FW I'm totally clueless what to use to clean them.