Check out this website:
Earthrounders: round the world flights in light aircraft
Great resource for people planning an around-the-world flight with light aircraft. The majority of the people who have done such a flight are also very open about what routes work well, where to avoid, etc.
One thing to keep in mind, the availability of AVGAS continues to shrink around the world, if you can help it using an aircraft that can operate on Jet-A is recommended. While it is possible to do the flights using AVGAS, it definitely decreases your options considerably.
If you're wanting to do this flight for charity, I would suggest you get your trip well funded prior to departing so that any donations can go directly to the charity. Check out the websites of people who have done these flights in the past for lists of several suppliers who have been known to sponsor such endeavors.
amraam