When you move, set aside an easily accessible area for maintaining emergency supplies. Bottled water, canned goods, medications, and more should be included in your stash. Rotate your stock to keep it fresh.
I agree with others who posted about keeping your car's gas tank 1/2 full or higher and will adopt that strategy for myself.
There are hundreds of websites that describe what should be in an emergency kit. Search engines will point you to one that addresses the emergency you're most likely to confront. For me, it's earthquakes. For you, it might be interrupted power, floods, ice storms, or something else.