From personal and ongoing experience. I am in the process of working up a 8x57 mauser in a handi. I decided to go the rebore route using a donor 22-250 barreled action. Reason: Right or wrong, I wanted the quickest and laziest route possible on the metal work side. The 22-250 is a great candidate cause the case head is almost identicle in dimension to a mauser cartridge so that alleviates the ejector/extractor fitting. The exisisting 22-250 barrel contour meets the minimum dimension for a rebore. It was a tad on the pricey side, but for 350.00 + shipping costs Wayne York will do a fine rebore and rechamber job, and he has stood by his work if you should run into a problem.
I am sure the stub route will do just fine as well. You can buy brand new Green Mountain, or Brownells 6.5x55 mauser barrels for around the 80.00 mark + shipping from Midway or Brownells. I've never done a stub, so some of the other members who have can weigh in or mine the FAQs for info, to find a suitable stub w/underlug that can take the pressure.
I am currently fitting a custom made stock to this action, but will be making a some mannlicher stocks from a chunk of walnut that I have recently acquired. I plan on the 8x57 wearing one of these at some point in the future. Best tip I can impart is take your time with it and have fun. Please keep us updated.