just my 2p here, if you carry on, you will get it a mirror, it's not to do with qualities of metals... but you REALLY need a bench polisher, if you don't plan on getting one its best to settle on the fact youll never get it a mirror shine, it's just not time or cost-effective by hand, or carry on through the grits to get it looking a lot shinier. if you work hard and long enough you can get even super ****ty metals like diecast (a mixture of metals, normally contains zinc) to a high shine. There should be nothing on display on a pinball machine that you can't get to a mirror shine if you so wish.
by a mirror, I literally mean mirror, not just shiny but can see the micro-scratches.
it's hard to tell you what grit to start at as don't know how bad the scratches are to begin with but work all the way through the grits.
your basically making the metal smoother as you go through the grits, making the set of scratches from previous grits disappear as you go. it takes HOURS.
when you're ready for polish, there is a compound that goes on the buffing wheel, there are several types which are different colours depending on how scratched the metal is.
If you're looking for brushed, scotch pad (green then red) will serve you well.