Standard 'industrial' finishing of stainless steel is to flat-sand with progressively finer and finer grit
eg. 80 ---> 120 ---> 180 ----> 220 ----> 320 grit (to remove all scratches from the previous grade of grit), then buff with 'tripoli' (a white 'rouge' that contains crushed 'diatomaceous earth / DE', .... sometimes known/named as "kieselguhr")