So, for convenience you decided to travel by plane, at least for the longest legs? Fair enough!
Buying tickets as you go
But if you have constraints regarding where and when you want to go, you might end up with little choice but to pay an expensive fare or have to build a trip including many transits.
Buying a world-tour ticket
Also there are a few restrictive rules, such as, you can only travel one way (East to West for instance) and cannot change back and forth between hemispheres. I mean, you could, but you’ll have to pay extra, losing some of the benefits of this ticket.
And more important: it is often limited in time, usually one year, so you cannot extend your trip!
The solution? A mix of both!
However, regarding intra-continental flights I would look into tickets individually and compare with other means of transport. The main reason for that is that it would allow you to use local low cost companies that are not part of the major alliances. For instance, Air Asia travels to many destinations and usually offers great deals, especially from Thailand.