Brushed Stainless Steel

Brushed Stainless Steel
What's the easiest, most effective way to POLISH stainless steel after wire-brushing it?

It's a 316 stainless panel. I don't want to ruin it buy trying high-fine sanding, unless this is the best way. I want it to be glossy.
The metal is clean and free of tarnish, since I wire brushed it. The problem is, that chemicals will not affect the surface. I'm looking for a way to smooth this extremely hard metal surface. I want to know how to "buff" it I guess. By polish, I don't mean to get rid of tarnish, but to create a mirror-like surface. Someone out there has to have buffed metal before!

Depends on what you are working on to some extent. For general stainless steel polishing, I have good results with Brasso (hardware stores sell it). For very fine items, you might wish to try Flitz Polish (the cream not the liquid).
Flitz is also sold at larger hardware stores.