Wood finishing for a vintage Weiman Dining Table

Hi there
I am restoring my grandma's mid century dining table as a present. Anyone experienced in vintage furniture restoration who can guide me or offer their services? What type of sander and preservatives can I use? here's a pic of the table

That is actually a game table and you may destroy the value if you do anything more than simply refresh the finish with something like linseed or danish oil. It was probably lacquered in the 50’s and it may be hard to match the lacquer. However, a light oil coat rubbed with a microfiber cloth will restore some of the shine without totally changing the look. Test on the lower leg first.

Well, I can't claim any significant knowledge of wood finishing, but I would be reluctant to take any but the very lightest abrasives to that. Simple cleaning and polishing would make a big difference.

Can you show us close-ups of any particularly bad spots?