From our experience without services following the Christchurch earthquake, the follow are things you should try to have.
A gas barbecue is really useful.
Keep several torches and spare batteries. Really important if disaster comes at night. Spread them around the house. We had both ours in our bedroom, but the bedroom door was jammed shut by the earthquake. That could have been a problem, if the earthquake had been at night.
A portable radio is essential, as it is the best way to keep in touch with what is happening elsewhere. Make sure you have plenty of fresh batteries
Solar lights are really handy. In the summer, we had bought several solar-powered garden lights to light up our drive way. They cost less than a dollar each. We put them outside during the day, and brought them in at night. Each one put out as much light as a candle, but is much safer. I also bought a couple with three LEDs, which are strong enough to ready by.
Keep plenty of food. Dried and canned food keeps for a long time and is great to have on hand.
A chemical toilet is essential. Some really cheap options are available from China. We have a Porta Potti. They are a great design. Having a solution to the number one problem under your control makes life bearable and reduces the risk of disease enormously.
Get to know your neighbours. When disaster strikes they will be more help to you than relatives and Christian friends who live a mile away.
The internet is wonderful for communication. Make sure that you have a way of accessing the internet that does not depend on electricity or telephone lines, because they may not be there when trouble strikes.
A small portable generator can be really useful. They are made really cheap in China now. We have been lent one, but I think I will buy one when this is over. You can do so many more things when you have access to electricity. Some solar panels to charge batteries might be a cheaper option.
An old telephone is essential. The cordless versions we have come to love do not work when the electricity goes off, even if the telephone lines are still working.