The South Island is better. It has more remote regions, it has more mountains, it has fewer cars amd fewer people. Every time I ride I learn more about the optimum setup for my bike and equipment. The only way to learn that is by doing it yourself. You should spend a week riding locally to learn how your bike and equipent is going to handle a longer cycle tour.
Dairies stock fresh milk, bread, newspapers, and groceries.
Most petrol stations are filling a similiar niche as dairies - they stock the same sort of things with a bit more emphasis on junk food. Petrol stations tend to be open for longer hours than dairies or supermarkets, some 24 hrs. You'll find a supermarket in cities, suburbs and towns. All the cities also have Macdonalds, Kentucky Fried Chicken and Pizza Hut. Oh, and they sell beer too.