In most of the bigger towns you'll find one or more of these supermarket chains:
New World, Foodtown, Woolworth, Countdown, Pak ‘n Save If you spend NZ$40 or more you will find a fuel discount voucher for a petrol station at the bottom of your receipt. It may be only a few cents per litre but at the end of the day after travelling approximately 10,000km over the next few months it'll still be worth it.
In the smaller towns you will rather find shops like Four Square, Super Value and Seven Eleven. Generally these shops offer all the essentials but it is recommended to stock up on the basics like coffee, pasta, toilet paper etc in one of the "big brothers".
For everything you can't eat – go to the warehouse! Extra towels, gas cooker, goggles, undies, cutlery, linen, portable radios etc – You won't get the greatest quality but therefore you won't end up broke either. Also second hand shops are very common in New Zealand and well worth a visit. Often you will find cheap pots, plates, cups etc with nothing wrong that a good scrub wouldn't fix.

Payment options

Direct deposit into a bank account as well as payment in cash or travellers cheques are common methods of payment in New Zealand. Credit cards are also widely accepted (unfortunately not by us though). Please keep in mind that a money transfer from overseas may take several days to be cleared at this side of the world. Also be aware that most bank cards only allow withdraws from an ATM machine up to NZ$800 per day and are not accepted for cash withdraws over the counter. That is only possible with a credit card.