The best size or type will be what works best for you or your family. There is no “right” or best answer.
But, some things you want to keep in mind:
1. Easy to carry or roll if lifting is a problem. Even children can carry their own if it is in a backpack they can lift. This is in case you have to hike out of where you are to seek shelter in another location. Worst case scenario, you have to walk, there could be trees down or debris in the road. So, think light and portable.
2. Waterproof: Here in FL, especially during the summer or hurricane season, when it rains, it pours. So, you want your kit to be waterproof. Ideas: Check boating supplies and camping supplies for waterproof bags. Or, just get a really big poncho and wear it over your pack. You can put every item in your bag into smaller plastic grocery bags or zip locks or all of it in a trash bag to waterproof your kit more economically. I recommend you do this anyway, that way if something leaks or spoils, it doesn’t ruin everything.
3. Economical: It should fit into your budget. It should work for you. You can always upgrade later. Really a double lined trash bag with items inside that are also packed in plastic will work fine until you can find something better. Goodwill and other places might have luggage or backpacks for less cost that would work just fine. Remember the idea is to survive, not fashion. Really, if it works, you don’t even have to like it. 🙂 Similarly, a big pillow case lined with plastic would work. Just sling it over your shoulder like Santa if you have to hike it out.
4. Size: It depends on what you are packing what size is best. You might wait to purchase or decide on your container until you have gathered all your supplies and see how big you need. Each item can be many different sizes: For instance: a heavy duty poncho is going to be much bigger than the flimsy pocket sized ones.
To save space, take off extra packaging. Squeeze out air. You might trying rolling clothing items or putting them in zip lock and squeezing out the air to save space.