Sleeping Bags
This is an essential emergency item.
Be sure to have one for each person in your party.
Sleeping bags can be used inside a shelter, or by themselves. If you have a good bag, and there is no rain or snow, it can actually be pretty pleasant sleeping in the open. But weather is unpredictable, and can't be trusted during an emergency situation, so it would be best to be in a sleeping bag in a shelter of some sort.
Temperature.
The first consideration in picking out a sleeping bag is how warm a sleeping bag will keep you. Unfortunately, there is no standard rating system. Each manufacturer has their own, which is good for comparing bags within a product line, but doesn't help in comparing bags in different lines, and can have little relevance to real world conditions.
What to do? Buy from a reputable manufacturer with a reasonable return policy that includes sleeping bags. Take their word for their rating. Try it out. If it doesn't do what they say it will, send it back and get the next highest/lowest rating.
Frankly, there are so many factors in making a sleeping bag comfortable to a specific person, it's impossible for anyone to say for sure how it will work for you. The difference in male and female metabolic rates alone is enough to throw off any calculations. And your own metabolism goes up and down depending on circumstances. If you have had relatively little food recently, your metabolism will probably be down and you will feel colder than if you have been eating well. In an emergency situation, chances are you are going to need a little warmer bag than you do right now.
So it's impossible. So relax. Take a your best guess, and see how it feels when you try it out. Realize that however it feels now, it will be different when you need it. Some bags have features that make you warmer or cooler when it's needed. The most common addition is a hood built into the bag, and I wouldn't buy a bag without one. You normally lose up to 60% of your body warmth though the top of your head. There are many other features. The more options your bag has, the more options you will have.
What if you get a bag that does not keep you warm when the time comes, despite your efforts? What if the temperature drops lower than anyone could have reasonably expected? What if....
The answer to all the 'what ifs" is to be prepared with options. I have, in addition to my own good bag, a few cheap lightweight bags that I can use for a variety of purposes (like putting one under another person who is bleeding and in shock, and needs to be off the cold ground right now). I could use one of those lightweight bags inside my own sleeping bag and be much warmer. Or it could get unseasonably warm, and I'd just use the lighter bag. I also have a hoodie. If pressed, I'd sleep in my hoodie, in the lighter bag, inside my own bag. With a blanket wrapped around all of that. And a tarp wrapped around that. You get the idea.
No Sweat
One thing to keep in mind is that your clothes retain the moisture you sweat. You can take a considerable amount of water with you into your sleeping bag if you jump into it with your clothes on... or even just your underclothes, which can contain over a pint of moisture by themselves. That includes your sox. As unreasonable as it seems, in most instances you will be warmer in your sleeping bag without the clothes you've been wearing. You can either just take them all off, or optimally, put fresh ones on before you get in. The upside to that is that you can wear that set of underwear when you get up, and they will be all nice and warm.
In cold weather, will you feel cold as you do this? Oh, my, yes. But it's worth it.
Waterproof
Most sleeping bags are not waterproof. That may seem odd, but it's difficult to make waterproof material that keeps the rain out, but also 'breathes', permitting moisture from your body to go out. And since the body constantly gives off a considerable amount of moisture, you really do not want to keep it inside the bag. Put your hand in a plastic bag and see how quickly moisture condenses in the bag.
But there are some sleeping bags that are waterproof and yet permit your body moisture to exit. They are usually more expensive. As I said, it's hard to do, and needs the latest in material technologies. Perhaps it is worth the extra. But that's your call.
Since most bags are not waterproof, you have to consider how to keep rain out of your bag. A waterproof shelter pretty much takes care of the issue. Without a shelter, an un-waterproof bag will sop up rain like a sponge.
In between are sleeping bag covers, which are essentially a plastic bag the size and shape of a sleeping bag, except a little larger. A good one is large enough to stuff additional insulation like crumpled newspaper or dry leaves for added warmth. You can fine one at Nitro-Pak
Pad
I suggest you get a pad to put under your sleeping bag. A good one makes sleeping on the ground so much more comfortable. There is no need to be uncomfortable, even in an emergency. Maybe especially in an emergency. A pad helps you get a better night's sleep, and for that reason alone I think having one is invaluable. I would not think of going backpacking without one.
Maybe that's why I'm fine with just a backpacking pad. I've spent many a happy night under the stars with one of those between my bony hip and the ground, and drifted off quite comfortably. An example is the Texsport Pack-Lite Pad
at Amazon.com.
That brings up air mattresses and air beds. If you are used to sleeping in a nice soft bed and maybe have never slept on the ground in the outdoors before, you might consider one of these. They do have the benefit of keeping you further from the dirt, and that is very nice in terms of rain and cold. I don't think of them as emergency items. But they may be for some people. If anyone in your party has arthritis or some other physical difficulty that would make sleeping on the ground a real hardship, perhaps they would be nearly a necessity. Remember that you have to blow them up. Get a pump. Definitely get a pump.
Under the Pad
The kind of pad mentioned above is plastic, so while it is not technically necessary to have a sheet of plastic underneath, it is highly recommended. Ground moisture tends to seep up, especially at night, and if just a corner of your bag gets off the pad, you could have a real dampness problem. Easy to make sure that doesn't happen. Just cut a piece of plastic at least one foot larger than your bag, and put your pad on that. Wouldn't hurt to be three feet larger on each side. Then you can lay out gear on the plastic. Or cut the plastic for some future use. Again, backup.
Thickness of plastic? The thicker, the more durable. I would suggest at least 3 to 5 mils thickness. Sleeping on a good tarp or in a waterproof tent or other shelter satisfies this requirement.