Presuming you are travelling with a US passport you won't even need to talk to an immigration official - you can just use the eGate and go straight through. You will need to talk to customs, but they are more interested in what you're carrying than you yourself.
Presuming you're travelling in/after October you will need an
NZeTA
The only way they are going to care about proof of funds is if you don't look like you can support yourself. If they do ask, simply showing them a credit card will normally be enough. Absolutely no need to have cash on hand.
Originally Posted by
Nayef
What about the other stuff such as asking for a return ticket and proof of accommodation? Do they ask about those more or less frequently than funds?
US citizens (and those of most non-visa countries, excluding Australia) DO require a return ticket unless you've obtained official permissions to travel without one, or have a visa. NZ Immigration won't be your issue if you don't have one as you will be denied boarding on the flight to NZ.