In the event of a large-scale disaster, you could be left tending to yourself and your family for up to three days. Due to the ratio of first responders to citizens, some of the less-critically injured may have to care for themselves until help can arrive.
That means you need to have enough supplies to last you, your family, and your pets for at least three days.
The #1 need for survival is water. The recommendation is 1 gallon/person/day. That means a two-person family would need SIX gallons of water in their kit!
Other needs like food and medicine are going to be a little more arbitrary to your and your family's requirements.
Don't forget about Fido either! Your pets will also need food, water, and other items.
When disaster strikes, electric services are often disrupted. Be sure you have backup batteries or power banks. Flashlights are often safer than candles so that you avoid igniting gas or other flammable substances.
Some weather radios can be powered by a hand-crank, solar power, or even old-fashioned batteries. You can also find weather radios that can charge your phone or has a built-in flashlight as well!