Some pretty deep scratches and dents can be polished out.
Dents, where the metal has just been displaced can first be worked over to push the metal back in place. That saves some effort of going deeper than necessary in making the damage disappear.
A smooth, flat faced punch & hammer or sometimes just a small flat faced hammer will do.
When first attacking the damage, don't be concerned with the direction(s) you are polishing to remove the marks. Any direction is fine and becareful not to dig a hole in the spot where the damage is. You have to feather the area out slightly into the surrounding undamaged metal.
When switching grits, that is the time to cross directions with the preceding grit used.
At least go 45* to the prior grit. That will let the new grit cut the high edges of the grit lines off cleanly and efficiently.
It's faster and will keep things flatter.
If you just keep following the same direction grit after grit, you will end up shining up the area but undoubtedly leaving some of the heavier grit cuts underneath the shine.
Cross-polishing instantly shows the previous grit marks and you can tell when they are gone. You need to do that or they will show when you put your final high polish of matted finish to the metal.
The directional grit lines, what ever direction you chose, can be established with the final grit. The finest grit you chose to go to. Use that after it is used to cross polish the grit before it to make sure those previous lines are gone.
Then simply re-establish those final directional lines in any one direction you please.
Always back your grit paper with a hard surface. I just wrap it around a worn smooth cut file generally. Others use a smooth wooden bloc or stick.
Just pay attention to edges and screw holes. Keep them sharp.
For the matted finish, grey or maroon scotchbrite works well. Use a little oil on the surface when the scotchbrite is used and a slightly more burnished effect will appear.