If I were to do such a trip I would either take a plane that can run on straight mogas (something with a Rotax 912 up front) or a plane that can run on straight car diesel & Jet-A (something with a Thielert or Austro). But not something that runs on 100LL avgas exclusively - sourcing fuel outside the Western world is simply too complicated and expensive.
More specifically, I'd take a DA-40 with the 155 Hp 2.0 Thielert and long-range tanks (~1000nm range). Or a 912 Europa with extra tanks, such as this one:
Europa N81EU
Thomas, by the way, did not cross the North Atlantic but did Azores to Newfoundland in one hop. I think it was a 13-hour stretch. If you're able to do it that way, you'll save yourself a lot of foul weather.
Of course there are a lot of people who have done round-the-world trips. This site offers a really good collection of them:
Earthrounders: round the world flights in light aircraft
easiest thing would be to take wings of stick in container
That would be another consideration. Can the wings be taken off relatively easily, so that you can either store the plane in a little unused (cheap) corner of a hangar somewhere for an extended period (while you sort out personal issues at home for instance) or put it in a container for shipping? Over the course of a year, circumstances might change dramatically, causing a change in plans.