When a disaster strikes that forces you from your home, you will have only two real options. Some disasters like hurricanes & earthquakes will likely have you ending up in a local public shelter. On the other hand, such disasters as nuclear attack, wild fires etc. could have you running out of state to friends or relatives.
Shelter life is usually short lived, but a favorable situation. Imagine being crammed into a school gymnasium with hundreds of others with only a thin mat and a few square feet of personal space. The food served will be a choice of two...take it or leave it, not to mention rationed and scheduled. There are some provisions you are going to want to make sure you have when you have to hunker down in a shelter. Have some extra water and something to flavor it. Single serving stuff is best as it can be hidden much easier in a pack or duffel bag. You will also want some snacks to supplement the food that is served. Again, big economy sized potato chips is not what you are looking for here. Look instead for cereal bars, fruit cups, things like that. A hand crank radio will help keep you informed when shelter officials don't have the answers. By the way, I will ALWAYS recommend hand crank flashlights & radios because batteries wear down and are expensive to stock up on. Canadian tire sells a great flashlight/radio combo unit that also charges cell phones forr about $15.00...I own a few and always have one in my briefcase. Keep entertainment in mind...have a book or two in the BOB to keep time running at a normal pace. Doesn't it always seem that time slows down when all you have to do is stare at walls or count ceiling tiles? Keep some travel sized toiletries in the BOB as well as TP, which may be scarce at a shelter. Don't forget a change of cloths or two, keep in mind you will likely be sleeping fully dressed...I know I would! Above all, keep food & water supplies out of site and NEVER leave your belongings unattended.
Your other option will be to travel some distance to shelter with friends or relatives. For this, you want to have a vehicle in good working order. Have some extra fuel on hand for tanking up before you hit the road and a 5 gallon or two to take with you. Water & food will be easier to carry in the car so larger containers will fit the bill here. Remember to keep them in a handy location and ready to go. Yes, once you get to where you're going, you will be out of range of the panic and supplies will be available, but given that you will not be the only one getting the heck outta Dodge, and roads could be a nightmare. Couple that with the fact that you may be taking a round about route and you need to consider a way to heat/cook your food. An inexpensive propane camp stove works well for this and two 1lb cans of gas should last you a few days. For the most part, your supplies will be the same as in a shelter scenario, just more of it. Your biggest concern is the ability to get where you're going. A tent & sleeping bags wouldn't be overkill if you may have to travel over a couple of days. Don't forget cash...gas stations along the early part of the route may not have working credit/debit card machines even if a generator gets the gas out of the pumps. All this is made easier if you go camping. Simply have all your camping gear neatly stored in the garage or in a garden shed so it is easy to grab. If you need to go long distances, everyone simply grabs the BOB's out of the front hall closet while Dad Or Mom get the camping gear and a food supply into the trunk.
In short, I would prepare for both scenarios...Have a BOB with the basics for shelter life, then a handy kit for long road trips near the car and ready to go. Don't forget to check over your kits on a regular basis to make sure food is not spoiled and that everything still works.