Search your desired flights with desired class. I find it a little easier to search one ways there and back because I usually move around a lot on vacation so it makes it easier to search for a route home when I have flexibility of airport (So I might land in Brisbane and fly back out of Melbourne - assuming they have flights available. I'll often map out which cities I can fly to/from and then plan ground travel around that) but then I'll book the final itinerary as a RT due to U
nited's Exclusionist Perk. So basically if I flew to Brisbane and then home from Melbourne a flight between the two cities would be free on a United partner. So you could go to Brisbane for 4 days and then take your free flight to Melbourne for another 6 days before heading home. The free flight could be anywhere in the United defined region as long as it occurs between your departure and return on your round trip (assuming they have award flight availability). Its also in the same class of travel as your first leg so if your first leg of your trip is in domestic first\intl business you get a free domestic first\intl business flight between your cities.
(We've done that many times. For example: We traveled to the Seychelles in business and then home from Nairobi in business. We were able to include a free flight from the Seychelles to Nairobi in business class because it was in the same United defined region)
1: Sometimes this gets reset when searching so make sure to use the drop down to select a different fare class if desired
2: If you have flexibility in date click on #2 to show a longer calendar of prices
3: "Business (lowest)" will often have an economy seat mixed in. Sometimes that is just a short positioning flight but sometimes its the longest leg which is not ideal. Click the "Details" option for the desired flight and it will tell you what cabin your seat would be in for each flight. "Business" is Domestic First\Intl Business the whole trip
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Amex points don't transfer to United. Chase does - usually takes 2-5min
According to that flyertalk thread there are a lot of options to SE Asia right now. I found a scattered few to Australia. None to NZ. Options existed for Africa and Europe too. SE Asia, Oceana and Africa would represent the best mile value for those that care about that