The best way of seeing a lot of the world at a reasonable price is to get a round-the world (RTW)ticket.
You make one fixed-price booking and you get a bunch of tickets for every leg of your journey.
Usually, there is a general route to take, and you have
a certain number of stops and a certain number of miles you can use. You can't go absolutely anywhere on a RTW ticket but they do offer flexibility.
Your travel agent should be able to help, or search online for
round-the-world ticket suppliers.
Normally you can change the dates on your ticket, with some restrictions (eg you can fly out of somewhere a month later, but not a year). Check when booking if there's a fee for changing the dates.
Altering the route is possible (within reason) - again, check how much this will cost.
If you make changes while you travel, you will have to get in touch with the airline directly, not your travel agent. It's a good idea to have the relevant information before you leave or you'll be bimbling about Bangkok trying to find the right office on a hot and sweaty afternoon.