How do I polish my beat-up Shimano cranksets?

I have some older Shimano cranksets that are still going strong functionally, but are somewhat beat-looking. Various scuffs from my shoes, assorted scratches, and ordinary wear and tear.

Some would say this gives the parts character, and I should leave well enough alone. But I would like to polish them up and make them shiny again, if it is not too much bother.

Never having done this before, I am humbly asking for advice from other riders. I own an electric drill, but do not have a bench grinder/polisher. So how do I polish them properly? And if I can make them look new again, what can I do to preserve the flashy finish?

Thanks in advance, and safe riding,
Joel Dickman