Nice! Good luck with your table, it looks pretty nice in the pictures, but you were focusing more on the machine. As for the machine itself, Ebay and Google for parts will go a long way. ID what kind of bobbins/feet/needles it uses, and you should be able to get all sorts of parts for it.
As for cleaning, outside cleaning can be pretty straight forward, dust it, maybe take a magic eraser to any stubborn spots (be sure to dry any drips.) Check the bobbin area for oil/goo/lint, clean that out. The machine itself will probably need to be oiled if it's been unused for more than a few years. As it's a straight stitch only machine, if I am reading up on it correctly, don't ditch your Kenmore entirely unless you really want to. Unlike your Kenmore (possibly, depends on the model,) the Singer can probably sew through concrete given the time.