2016 is a long way off. This game might be very different then. But assuming it is still similar, a coupe of strategies:
1. Read this post
http://travelisfree.com/2013/12/27/c...routing-rules/ as many times as necessary, and collect as many a total of 320K UA/Chase UR points in one account, or 160 each in two accounts. Easy with all the different Chase cards and office supply promos. Then book business class tickets that give you the bulk of your travel, say US-Africa(stopover)-Asia-US. Collect AA and BA miles, and use any leftover other miles and paid LCCs, to fill in the gaps.
or 2. Collect SPG and AMEX points. Fly to Brazil to start your trip. Using ANA miles, book a Star Alliance trip that begins and ends in Brazil, with 4 stopovers, as far as you want to go. Use AA and BA miles to fill gaps or for side trips. Fuel surcharges are illegal on Brazil awards, and ANA does not impose surcharges on any part of an award that begins and ends in Brazil. Skip the last leg if that's convenient.
3. If you can do the spending, get AA Exec cards for as long as you can. It's just crazy not to. The best strategy today might be perfectly useless by 2016.