I have done a dozen or so by hand and the following is my method.
I use an air orbital sander and use progressively finer grades of wet or dry sand paper. I start with 350 or 400 depending on the finish from barrel maker. I cut circles from the paper and spray glue them to the face of the orbital. When the paper is fresh, you will get some scratches, as the paper fills it will start to polish more and scratch less.
Wore down 600 will give you a pretty good finish and may be enough for you. All depends on your eyes. If not, go to 1000.
To polish, I use strips of blue jeans a little over an inch wide and coat them with polishing compound like Mothers, etc. I wrap them around the barrel and pull the ends back and forth, back and forth, back and forth.......................back and forth.
This is when scratches that haven't been sanded out will show up. Don't fret, go back to a wore out piece of 600 or 1000 and remove them. Then back and forth some more.
Final finish is a pure cotton rag with polishing compound and polish the barrel lengthwise, not around like previous.
It is labor intensive, but the results are excellent.
Jim