When I did mine [they were pretty bad ] I started with 800 grit paper and worked up to 5000k stuff, finishing off with polishing compound [G3] on a small wool pad on my DA machine - the results were very impressive, if I say so myself!
I'd disagreed with that video 'still' though - received wisdom is to work in straight lines, changing through 90 degrees with each change of wet 'n dry paper grade.