A bug-out bag or 72-hour kit is a collection of items one would need to survive for three days as occasioned by a disaster. The focus is on evacuation from an immediately perilous situation rather than long-term survival. The collection needs to be handy and in a form that can be carried without impeding the carrier's ability to reach safe circumstances.
All collections are designed to support the Big Four: water, protection, food and knowledge. Knowledge comes into it because a disaster plan for getting from an unsafe situation to a safer one, must be had beforehand.
A 72-hour kit for family emergencies, whether carried individually or together, might have a slightly different list of contents than a grab-bag carried in a car to support rejoining one's family in a time of crisis. This is called a "get me home" kit by some.
Obviously, not everything is quite as timely as the basics. Little attempt is made to prioritize this list. It's provided as containing items that should be considered, tailored to individual situation, and not necessarily of crucial importance.
A really convenient way to package this kit is a 5-gallon bucket with sealed lid. However, think about carrying a 72-hour kit: it contains at least 3 gallons of water (which weigh in at 8lbs per gallon) and everything else. This would amount to having to carry 2 buckets. Now imagine your 5-year old doing that.
Carrying a bucket isn't the way. You would do best obtaining Alice packs* with frames for your family. These can be had at places like Sportsman's Warehouse or even less on-line starting at $35 plus frame. One or two should be of a quality to transfer the burden to the hips enabling the wearer to carry much more, perhaps a parent carrying a child's water, etc.
If you need to reach a retreat under adverse circumstances and will have to travel, avoid solutions that are garishly colored and would draw attention.
Then again, if you're pretty certain not to need to travel, you're lucky and can resort to the 5-gallon bucket solution: holds a lot, is waterproof when properly sealed, keeps contents safe and stacks nicely.
You'd be surprised how inexpensive and convenient some items can be. For example, Home Depot is a good source of rope and/or paracord. It is cheap and comes bundled in many lengths, packages, colors and gauges.
A good Leatherman™ can be had for $30-$90. It's a one-time purchase.
We all like to think we live in a civilized world in which neighbors, passers-by, etc. behave decently with no malicious intent... (recommendations to come)
* All-purpose lightweight individual carrying equipment.