Read the stickies on cleaning and oiling your machine and watch Muv's videos. Your machine is newer but the same advice is good for all machines. Use sewing machine oil or triflow(?) only. Other oils are too heavy and will gum up faster causing problems later.
I haven't been inside of those machines. If it has plastic gears don't oil them. Some plastics react with oil and can be damaged. If there's grease on them use a good light synthetic grease like triflow grease. If they don't have any grease on them leave them that way.
Those old Kenmores are good sturdy machines. I don't think it will need much more than a good cleaning for it to work well for you.
Rodney