So I don't plan to sail around the world, but I can still think about what boat I might select. I think Dazzler's suggestion deserves a close look; Tom designs good boats and Westerly built good ones. The Fairweather 39 down south, too. I would forget old cruiser/racers because, well, they're old. And used. And probably passed through owners who haven't kept them up, kept their equipment current, and frankly mistreated them. Too much work, too much that could go wrong. Too much like the current batch of singlehanded rounders whose old boats are failing them.
If I were serious about a circumnavigation I'd have to decide between speed and comfort. Speed would mean looking at boats more race dedicated than cruise oriented. If I wanted to sail on the edge and had the bucks, I'd be looking at recent ocean racing veterans and be prepared for minimum comfort (no teak). If I just wanted to "sail around the world" in a reasonable amount of time I'd look at the two boats above for starters. And several others that have been suggested.