I'm very envious - you're sure to have a great holiday in NZ.
As to airlines, it depends on what you mean by 'best'. Cheapest could well be via Japan (and you can smoke on the flight, in case you're fed up with having to 'step outside' in DUB). Fastest is via SIN, which saves a couple of hours over the comfiest, which is NZ1/2 via LAX (decent seat pitch in Y and friendly rather than grovelling service).
Personally I'd go for NZ1 - take some knockout drops once in your seat and wake 24 hrs later in Auckland ...