Membership in the AA has a lot of benefits including breakdown assistance, discounts and travel information. If you are renting a car you may already be covered by some sort of breakdown assistance scheme, so it is really only worth the money if you've bought a cheap old car that is likely to break down. Because there is a lot to see, many travellers buy a car, drive around New Zealand for a few months and then resell the car to another group of travellers. This is a good option for a group of people with time on their hands, although both car and motorhome rental are both popular options. If you want to buy a car, check classified ad magazines in newsagents and petrol stations and noticeboards in hostels.
Most hostels have a few cheap cars for sale.
Depending on the length of registration remaining on the car, you may also need to pay for more registration and third-party insurance. Renting a car or motorhome is a much easier option. New Zealand has all the major rental companies plus a lot of smaller car rental agencies which often have much better rates. However you may need to stick with the major companies if you want a one-way rental, particularly if the car is being dropped off in a different island. Generally inter-island rentals entail dropping the car off in Picton or Wellington and picking up another car when the ferry takes you to the other side off Cook Strait.