Do yourself a favour and don't collect your vehicle when you're still jet-lagged. You are better to either have a stop over in Australia or spend a night in a hotel after you arrive in New Zealand. This way you can go sightseeing in the city without any parking worries and arrive at the vehicle rental station relaxed.
Although we'd booked and payed for the campervan and insurance from home already, they tried to put an extra insurance on us. This is not what you need when your only wish is to get some sleep.
If it's your first time in a campervan it's important to understand how to handle things such as gas, water/ waste water and power, and how to operate the controls. After our 24 hour flight we didn't understand all the instructions spoken very fast and with a lot of slang (as we are not native English speakers). Nor were we in a condition to ask our guide several times to speak a little bit more slowly. Later at the campground, we were glad for some friendly advice.
Take your time checking the vehicle. Any dents, scratches and other defects must be noted by a member of the rental company. Also, make sure everything is functioning properly.
Don't forget either that you have to drive on the left directly after the vehicle handover. We found the New Zealanders to be thoughtful drivers and traffic in the cities isn't too busy, but you have to get used to (if you aren't already).