Stuart,
When I do my polishing I start with 180 grit wet/dry.then go higher and higher 320/400/600/1200 by the time you get to the 1200 its pretty shiny already then when you buff it it comes out mirror smooth,it takes some time but once you see how nice it is you'll be happy with it.you can save some time by starting with the finest grit that will still do the job.
Greg