Peter:
I recommend the following:
1. Have the anodizing on all aluminum parts (stem, seatpost, crank and brake caliper arms) professionally removed. 2. Hand polish the good condition items yourself. If hand polishing doesn't work (using simichrome or mother's polish and rags only) then bring the part in to be professionally polished. 3. Have the anodizing professionally redone when complete. Give instructions, and better yet, bring in an example part with the sort of finish you want (shiny bright or more opaque/patinated, depending on your taste and apparent age of the bike).
For rare or vintage parts, I believe that it's better to pay for experienced polishing rather than learn the hard way and screw something up yourself. The critical thing is to be very explicit in your instructions (do it it writing, and discuss in person as well). Ask your local bike shop(s) for recommendations on both anodizing and polishing houses.
Also, for what it's worth, for collectablity, or "authenticity" it is probably better to leave things alone. Personally, I prefer to do a restoration to get most-like-new appearances.
My $0.02.
Andrew Gillis (raining in Long Beach, CA)