Deep scratches and broken edges are a bad sign. If you want to learn about stone polishing, this would be a good learner project. Don't expect to be able to craft a Michelangelo. A matte finish would be reasonable, and expect to leave the deeper scratches in place.
Matte marble finish should be polished out to 1500 grit. Gloss finish out to 3000 and buffed
These diamond pads are meant to be used wet and no higher than 4000 RPM. Buffers are the usual motor, but there are a few angle grinders that are variable speed and slow enough (Metabo and Makita).
A velcro back is handy to changing the pads.