You can buy a first aid kit in just about every drugstore, grocery store and even sometimes at garages. The problem is that the ready made ones just have the bare basics and are generally not sufficient to meet the needs of a growing family. You will find too much of some things and too few of others. You are paying for all of it though so it makes sense to pay for what you need the most.
The kit needs to be stored in a dedicated container that is capable of keeping air and moisture out. This can be in the form of a plastic storage box or bag, depending on what you need it for. If in doubt, use Ziploc packets to keep individual items safe and clean.
The kit needs to fit in with the needs of your family. If you have a larger family unit, you will need to stock up on supplies. Also consider the individual family members. Do you have a daughter who always manages to hurt herself and seems accident prone? Keep extra supplies on hand for her. Keep more of what your family is likely to need.
Of course, you cannot get away from the basics – you need to be able to treat wounds, gashes, burns, etc. Have something that can disinfect, something that can be used to protect and something that can be applied to continue fighting the infection. You will also need scissors to cut things, etc.
One section of the kit should be dedicated to medication. Some form of anti-allergy remedy and some form of pain killer is important. Consider a snake venom kit in need and possibly something to help with a troubled tummy. Through in some electrolyte powder and anti-diarrhea medication as well and you are pretty much set.
Also make a note of what the emergency contact details for your area are and add your mobile numbers as well – this must be attached in a prominent place on either the inside or the outside of the lid. The numbers should be clear and easy to read. The medical supplies kit needs to be in a place that everyone can find – your family must know where it is kept and that it needs to be kept topped up.
You also need to periodically check the kit for expired medicine. It is also a good idea to get into the habit of replacing any used items as quickly as you can. It is pointless to go to all the trouble of setting up this kit if you do not maintain it.