Rule of 3's
You can survive approximately:
3 minutes without air.
3 hours without shelter in a harsh environment.
3 days without water.
3 weeks without food.
Based on this information you are able to begin preparing efficiently by taking care of the most essential needs in order.
1.) Air - think toxic smoke from forest fires, chemical and biological weapons, etc. For these things a gas mask is one of the best ways to stay alive. I have searched around and found this site which sells a wide variety of gas masks and other air filtering apparatus, some designed for the elderly, children, and infants:
https://www.rddusa.com/product-category/gas-mask/
2.) Shelter - This is self explanatory. Most of us already have homes which provide adequate shelter, and for your bug out bag you may select anything from a sleeping bag with waterproof bivvy, to a hammock with mosquito netting, to a tent.
3.) Water - Many options exist to make water potable, ranging from a non-electric distiller unit for use in a home base or base camp situation to water filters and purifiers such as the Sawyer Point 02. I own this distiller and have had it for over 14 years, it still works like a charm and can make up to 16 gallons of pure distilled water per 24 hours:
http://waterwise.com/productcart/pc/1600.asp
I also own the Sawyer Point 02 purifier which filters out bacteria, viruses, cysts, protozoa etc.:
https://www.amazon.com/Sawyer-Products-SP191-Purifier-Assembly/dp/B0051HHNJ8
You will need 2 food grade five gallon buckets in addition to the Sawyer Point 02 purifier in the link above, and there is also a model that comes with 2 bladders that needs no buckets. This filter will clean a million gallons of water.
For my bug out bag, I currently have the Sawyer Mini filter which filters out all biological life forms EXCEPT viruses. It will filter 100,000 gallons of water:
https://www.amazon.com/Sawyer-Products-SP103-Filtration-System/dp/B00MPH1LEU
In addition to the Sawyer Mini filter, in my big out bag I keep a bottle of Polar Pure Iodine and some Katydyn Micropur Tablets, both of these will purify water infected with viruses, and when used in conjunction with the Sawyer Mini filter makes any water not contaminated with chemicals suitable to drink:
Polar Pure: https://www.amazon.com/gp/product/B00N5AGT1Q/
Katydyn Micropur: https://www.amazon.com/Katadyn-Micropur-Purification-Tablets-count/dp/B000H3DNF4
At our home, we purchased several water tanks, totaling about 3000 gallons, filled them and added enough Aquamira to the water to sterilize it, kept sealed after adding this the water in the tank is good to drink for 5 years.
Plastic Water Tanks:
http://www.plastic-mart.com/category/9/plastic-water-tanks
Aquamira water treatment:
https://www.amazon.com/Aquamira-Water-Treatment-Drops-1oz/dp/B000OR111G
4:) Food - For short term emergency food I favor the Mountain House Freeze Dried Foods. It tastes great, has a 25 year shelf life and can be made ready to eat in minutes with the addition of hot water. I keep a months supply of this for use at the beginning of an emergency situation. Unfortunately it is VERY expensive, at Amazon, which is the cheapest place I have seen it, you will spend about $800 for a 1 month supply for 1 adult, so it is not feasible to count on this for long term survival. For this we store rice and beans, potato flakes, corn, lentils, and other shelf stable foods in Mylar bags with Oxygen absorbers which are placed in food grade 5 gallon buckets. A link is provided below which teaches you how to seal your mylar bags with a standard clothes iron. We have an entire room stacked from floor to ceiling with buckets of food. To cook in a long term survival situation, we have selected the Solo Stove Titan, which can be fed dried twigs, dried grasses, etc. For short term/beginning of emergency use we have a Coleman Propane Stove that uses the 1 pound propane cylinders, these are cheap and can be refilled with a special valve from 20 pound cylinders, which we currently have 3 of.
Mylar bags with Oxygen Absorbers:
https://www.amazon.com/Dry-Packs-10-2000cc-Oxy-Sorb-Absorbers-Dehydrated/dp/B001Y0Y8C6
Food Grade 5 Gallon Buckets:
https://www.lowes.com/pd/Encore-Plastics-5-Gallon-Commercial-Food-Grade-Bucket/3694238
Lids:
https://www.lowes.com/pd/Encore-Plastics-12-5-in-White-Plastic-Bucket-Lid/3382566
https://www.lowes.com/pd/Encore-Plastics-12-in-White-Plastic-Bucket-Lid/50094688
Coleman Propane Stove:
https://www.amazon.com/Coleman-2000020943NP-Classic-Propane-Stove/dp/B00005OU9D
Refill 1 pound propane tanks from a larger tank with this adapter:
https://www.amazon.com/Universal-Disposable-Regulator-Accessory-Cylinders/dp/B019CND6J2
Solo Stove Titan - Burns twigs etc.
https://www.amazon.com/Solo-Stove-Titan-Lightweight-Backpacking/dp/B00DBYT9BI
How to seal your Mylar bags with an iron:
The peace of mind being prepared to withstand any long term emergency is priceless. Many things can go wrong, and stores around the country generally have about a 3 day supply of food on hand for the communities they serve. Look how quickly shelves get emptied as a hurricane approaches. You can start out with getting prepared by acquiring a 1 month supply of food, and build from there. Different sources recommend different levels of preparedness, the Mormon church, which my niece is a member of, recommends a 2 year supply of food and water be stored for each family member, for instance.