Hmm, "cheap" flights to NZ don't really exist!!
I have usually found the best and cheapest way is to keep an eye out for special deals on the Singapore Air website. These often come up in June or July for travel over the Christmas period.
Or to find out the cheapest (but often longest) way there, this website is pretty useful:
www.momondo.ch
Also, its always much easier to fly from Zurich as it means only 2 flights each way compared to 3+.
Oh, and unless you are planning a long stopover somewhere in between, make sure you book both flights with the same company - if you have a delay on the first leg of the trip and miss the second flight you will be covered and the airline will help find an alternative...book through two different companies, and you are on your own!
Hope this helps a little
P.S. Can I come too?!?!?