A good first aid kit is indispensable. I'm not talking about these little car kits, although they're better than nothing. I'm talking about a footlocker's worth. Think of being snowed in, no way to get to the hospital for the next 3 days and you have someone (yourself) have a heart attack, a stroke, broken arm, leg, hand or foot, major 3rd degree burn when the Coleman gas stove overturned, or accidentally cut a major artery when the kitchen knife slipped. I'm not saying you need to have a major surgical suite set up or need to be able to suture wounds yourself, but enough to hold someone together long enough to wait it out for help to get to you or to dig yourselves out to get help.
Food. Pre-cooked, canned food, dried or freeze-dried lasts longest. You need extra water for the freeze dried stuff though. Fresh veggies and fruits will only last a week at most. Fresh meat, only a couple days at most, unless the temps are below freezing. Cooked meat, add a day. Unless you have a generator with several days of fuel, don't bother stocking up on frozen foods during the summer.
Water. I have 27 gallons in plastic Jerry cans for my wife and I for cooking, drinking, and cleaning. That's NOT for flushing toilets with - I have a 40 gallon trash can that I fill with water before a storm, or can fill a couple buckets at a time from the nearby river. Keep in mind that 40 gallons of water weighs 320 pounds. 50 gallons is 400 pounds. Make sure your floors are strong enough for that much weight in a small area.
Shelter. The house is well insulated. I have a wood fireplace that I can keep going for several weeks before running out of wood that will keep the house warm enough that the pipes don't freeze. And if necessary, I can drain the pipes before that happens. I can also drain the upstairs zone and close it off so I don;t have to heat as much volume.
Clothing. Be prepared to wear your outside clothes inside the house in the winter. Keep your clothes dry and if they get wet from rain, melted snow, or sweat, change them immediately! That means you need a couple changes at least. Change your under clothing daily; they collect sweat, hair, pieces of skin, etc. Clean dry socks, undies, and t-shirt will reduce the chances of skin infections, keep you warmer, and make you feel better all around, even if your jeans and shirt are so soiled they can stand on their own.
Get a couple of crank lights and radios. You may run out of batteries but you never seem to run out of the ability to turn a handle. And there are some very sturdy models out there that will run a long time on just a little charging.
Put your emergency gear and supplies in a protected location, in containers, where everyone in the family can reach it without a lot of trouble. Someplace that won't get flooded, and you can reasonably reach even if the house gets blown down.
Weapons (i.e. firearms: shotgun, rifle, or pistol). This may sound crazy, but for most of you, don't bother. Only get a weapon if you're going to use it to hunt and kill animals for food. Or if you are 100% certain you have it in you to kill someone. If you have any doubts, confronting a desperate person or group is NOT the time to find out you can't do it. They'll take the weapon and use it against you.
I'm not much of a prepper. But I am a veteran, a hunter and camper, and I was a Boy Scout and a Scout leader for many years.