Stainless steel polishing dilemma

I have purchased multiple stainless steel parts that I need to assemble for a medical device. These parts range in size from 21 x 2.5 x 0.25 inch to 12 x 7 x 8 inch to 5 x 1.5 x 0.75 inch. I am welding this device together so that it's final dimensions will be 24 x 24 x 8 inch. My question is what would be the most cost effective to clean up this raw T304 stainless to make it shine and look professional - example - clean then weld, weld then clean and how should I clean (tumbler vs chemical etc...). please advise

You say this is a medical device; therefore, it sounds as if smoothness is the most important factor and the best way to accomplish that is via a mechanical process. If the part does not require a 6 to 12 RMS, then there are alternatives that are less expensive.

You can try finishing it in a centrifugal finishing machine wherein the mirror finish you require can be easily obtained in 2-3 steps depending upon the input samples.