Think of the main things one would need in a survival scenario remember Maslow’s hierarchy of needs?
1. A source of heat and light (fire)
2. Water
3. Shelter (what if your roof blows off or you have to evac your house?)
4. Food
5. Defense (optional, depending on the type of trouble you are expecting)
In that order.
First, let’s address the issue of heat and light. It’s a good idea to have a dynamo powered flashlight. These don’t require batteries and often double as a radio. You should also keep a supply of Bic lighters (cheap and easy to use) and some waterproof matches as backup, or a magnesium fire starter. If it gets bad enough that you have to build a campfire somewhere, you shouldn’t have a problem finding fuel for your fire.
Now, for water. You can buy it in packets by the case, or just buy several jugs, multiple gallon drums, or cases of bottled water. You should have a backup way of obtaining water should you have to get on the move. I recommend iodine (found in first aid kits, commonly) and filter straws, but UV water purifiers and water purification tablets are good also. Keep in mind that none of these methods actually filter sediments from water. That you will have to learn to do yourself.
Depending on the disaster, you may or may not be able to stay in your home. If you are forced to leave, or your home is somehow damaged or compromised, you will need shelter. Tarpaulin and paracord makes a good makeshift tent and other building materials can be scavenged. It helps to know how to make a shelter should your materials somehow be compromised.
Food wise, it is good to have a stock of canned and nonperishable foods. Be sure to cover the main food groups, if you can, as well as small, high energy snacks like M&Ms. It’s also a good idea to have some MREs around. These meals are high in calories and come with their own water-powered, catalytic self-heaters, as well as tasty side treats and useful items.
Now, for defense. Since you live in New Zealand, this shouldn’t be much of an issue. I don’t know what gun laws are like in New Zealand, but it would be prudent to invest in some type of self-defense weapon that can be used to protect yourself from anyone who decides they might want your stuff and aren’t willing to politely ask.
In addition to the above mentioned necessities, there are several other items that would be prudent to have in case of disasters.
These include:
A good first aid kit
Blankets
Pain, indigestion, and other medications and prescriptions
Rope (I highly recommend paracord because of its versatility)
Cash and important documents
A good folding knife, fixed blade knife, or multitool
Candles
Batteries
A small mirror
Fishing lines and hooks
Superglue (can be used in a pinch to treat severe wounds)
Duct tape
Soap and toiletries (especially toilet paper)
Plastic bags
EXTRA SOCKS AND GOOD SHOES/BOOTS (note the emphasis)
Warm outerclothes
Spices (salt, pepper, etc.)
The list could go on…
Here is a link that you may find useful.