Polishing stainless shaft

[nathanclymer]

I'm completely new to polishing and surface finishing. Most of what I do is good enough if the mic reads right and it looks OK. I have to make a shaft (which will hopefully turn into a production job) from 303 stainless. 25mm OD, tolerance of +/-.0005" X 7.5" long. The surface finish is 12 Ra. I'm making this from a piece of 1" round bar so I only have about .015" to take off the OD. I take one pass to clean up the bar, and one finish pass in the lathe, but there just isn't enought for the tool to "bite into" so I'm getting a little bit of chatter. I have an old (1940's) Cincinatti tool and cutter grinder that I should probably use for the OD. Now for the questions, what kind of grinding wheel would I need? How much should be left for polishing? What kind of polishing wheel (a cloth buffing wheel looks good to me)? and What kind of polishing compound? I have have an idea of what the roughness average is, but no reference to know what it looks like. None of the surface comparitor guages I've found go down that fine. I may be able to pay a lab to test it for me, but I hate to have to take it in, and then pay them to tell me its not good enough (polish, test, repeat until bank account is empty). The plan as it is, is to leave .001" over when turning. Mount on tool and cutter grinder with a scotchbright wheel. Put a buffing cloth on the same grinder and buff for a long time. Then have it tested. Doesn't sound like the best plan to me but it's all I've come up with so far. Any suggestions at all would be greatly appreciated.

Thanks
Nate