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...the wheel in your photo looks like a standard 700c road wheel. That's the most likely candidate, and they are pretty much all the same, as far as rim diameter and compatibility with your brakes. Hubs are different widths, and a 7 cogged wheel in back would be matched with a 126 mm distance between the rear dropouts, assuming they are correctly aligned and that was how the frame was originally made. There are a few (very few) steel frames that were contract built in Italy using standard BB shells and threading. It is unlikely yours is one, but as suggested, measure the width of it. Italian is 70mm wide, standard is 68mm wide.
None of what you have suggested is all that difficult to do. Take your time, and if you hit a snag (like checking and measuring frame alignment....which you should do before you build up any steel frame. Stuff happens to them if they get used, and if it's been sitting without wheels for long, or is getting shipped to you without wheels or dummy axles, the chances of this increase.)
Polishing a bar is a waste of time and energy. You're going to tape over it anyway with bar tape.
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