Usually when you are bringing a surface up to a mirror finish, you need to wet sand.
So you are going to need a powered sander that wont electrocute you!
A good choice is an air powered sander. You can get them in Block or Disc styles.
I use both, but for flattening, I like block. The larger the block, the flatter the sanding stroke.
As you probably guessed, air sander connects to an air compressor. Adjust the stroke knob to find the sweet spot - too far in either direction and it won't stroke at all.
You can also use an electric sander, again the larger the sanding surface, the flatter the stroke. Just make sure your sander is rated for wet use.
Buy sandpaper that says wet/dry on it, most fine grades are wet/dry, but there are exceptions.
Wear your respirator. Yes, I know wet sanding is not very dusty, but the dried slurry and the polishing compounds are bad for your lungs.
If you want to wear a Tyvek suit, don't contaminate the one you use for spraying. Maybe use an old one that has a taped up hole or two.
Make up a 2 liter bottle with about a 1/4 drop of liquid dish soap. You want just a little bit of soap. Just enough to break up the surface tension, but not enough to make suds.