A good emergency kit should fit inside a backpack, dufflebag, or small suitcase and shouldn't weigh more than 25lbs. This will allow it to be easily grabbed and taken with you during an emergency or other disaster and allow you to easily store it anywhere you go.
A good emergency kit should have several pairs of clothing. Such as a pair of shorts, t-shirt, nice shirt, sweater, pants, extra socks and underwear as well as a rain poncho or similar clothing item. A blanket and towel would also be good things to include in the bag if there is enough room, with a blanket being more important than the towel. A good space blanket would be a good addition if space is tight.
It should have enough little food items to last a person a couple of days (MRE, a couple of canned microwave meals, spam, beans, etc.), a good plastic or metal water bottle (it would be a good idea NOT to fill it beforehand since it could leak). Package of kleenex, a spare bathroom kit, flashlight, sewing kit, a small pan or pot, some spices and seasoning, and a smaller version of your travel survival kit.
Another good thing to include would be copies of all important phone numbers, insurance information, and other items that would be needed in case of an emergency situation in a secure waterproof bag. These should be kept safe in as hidden of a compartment as possible.
Once you have your survival bag packed and ready with all the items you feel would be needed in case you had to stay away from home for a week or more. You should place the bag in an easy to get to spot that is near emergency exits for your home or apartment so that you can just grab and go (although NEVER risk going into a dangerous area to retrieve the bag!).
Another option is to leave the bag in the trunk of your car. That way it is always outside the home in case of fire or natural disaster. However if there is a car accident or the car is destroyed somehow, then it would likely be lost or destroyed as well.
But no matter where you keep it, in the home or in the car, you should keep it in an easy to get to location along your escape route (which all families should have anyway)