Sorry to take so long to reply, I've been busy getting ready to leave.
I wouldn't be flying yearly, so having points that don't expire quickly would be important. I will get back from my trip at the start of next year, and probably won't take another big trip for about 3 years. I may, however, go to New Zealand within a year or so of returning.
My booking class is S when flying with Thai and H for the other bits of the trip. However, I would probably usually fly in lower classes, but I had to go a bit higher than I would have liked because I had specific dates I needed to fly on. Is there any other info that you need to know?
So most people seem to think that UA or OZ would be best?
Thanks again for all the help everyone has given so far.