Good morning from the future! To get to Europe from NZ is long haul x 2. I always fly in one long day, as I find that breaking up the flights doesn't help jet lag - it's just increases the amount of checking in, checking out, weird times zones and generally not enough time to see anything in your stopover destination. I'd rather have more time in the final destination.
I have so far flown directly from NZ to Europe via the USA, via Japan, via Thailand, and via Dubai. Dubai being my current preferred, because you have so many options into Europe from there. USA least favourite because of going through LAX. Time wise they are all pretty similar at around 24 hours of flying. For example, on Emirates i'd leave my home town and fly to Sydney on a Monday at 6pm-ish and travel west 3ish hours to Sydney and then back on to the exactly the same plane for 14-ish hours to Dubai, then connect in Dubai for another 7ish hours to somewhere in Europe arriving around 1pm the Tuesday. I find doing this that the jet lag is normally very manageable.
Another thing about flying from NZ. The planes are a good size, modern and decent airlines. Full service included. Eg. Emirates fly from my home town on an A380.
I just tend to zone out, enjoy the food, movies and sleep as much as I am able. It is normal to check your bags and not see them again till your final destination, it is also very normal to recline your seats after the meals to snooze.
And the cost...it's interesting but I notice the cost from NZ to EU return is often cheaper than NZ to USA return. At the moment I'd pay around $1800 NZD to EU return on Emirates economy - which is around $1200 USD. You do see cheaper, but usually with terrible connections.