Living on the gulf coast of Florida, I have personally weathered many such storms and stayed in my own home. I have a basic list of supplies and tips that I found helpful when having to deal with this situation. The majority of these items can be bought at your local dollar store or in bulk at your local mega mart or warehouse super store for super cheap or reasonable prices.
1. First and foremost, you have to have plenty of food and water for your family and pets. Your supplies should be enough to last from three to 7 days. Your water supply should be about 1 gallon per person per day. Buy a variety of canned and shelf stable foods such as meats, milk, veggies, and fruits. MREs (meals ready to eat) are also good to keep on hand as well in your kit if you have the means to acquire them. Do not forget Fido and Fluffy, they need food and water too.
2. Flashlights, candles, fresh batteries, waterproof matches or lighters, gas lanterns (for outside use only) are all very good to have on hand. The dark is a lot darker when there is no power in the whole area. I found flashlights that you shake to charge to be very handy since they do not take batteries. I found these at the flea market for a dollar a piece. Also, if you can, get one of those weather radio/flashlights that crank to charge. That is a handy item and you can get updates on the weather.
3. First aid kit is also necessary to have in case of injuries. You can buy readymade first aid kits with basic essentials or build your own. Regardless of which way you go make sure you have plenty of bandages, gauze, and tape, antiseptic of some sort, and peroxide, antibiotic ointment, pain medicines (acetaminophen, ibuprofen or plain aspirin) and any other necessary medicines that your doctor may have you on.
4. A gas or charcoal grill, lighter fluid or a starter chimney and paper, extra charcoal or gas or a fire pit with a grill so that you can cook your perishable food or sterilize water is essential as well. Unbelievably, you can cook anything on a grill if you have to.
5. You will need tarps and ropes or bungee cords to cover any damage to your home.
6. Ice chests and ice. If you are lucky like me and own a deep freezer with a drain valve, this is a perfect ice chest for emergencies. They are insulated better than most coolers and you can put extra ice in the bottom under your food if you know a hurricane is coming and drain off excess water if the ice starts to melt.
7. Cash! You should have plenty of cash on hand in a safe or lock box just in case. Remember if the power does go out the ATM will not work either.
8. Fill all your vehicles with gas. Gas pumps are electronic too and it could be a few days before power is back on in your area.
9. Emergency phone that plugs into the wall jack (not wireless) and /or charged batteries for your cell.
10. A handy item to acquire when you can is an inverter. It plugs into your car cigarette lighter (the aux jack) and when you turn on your vehicle, you can power some small items such as a fan or a lamp with it by running an extension cord from your item to the inverter in your vehicle. I did this to power a small TV during Ivan to see the weather channel during Ivan. It will not power your household appliances like a generator but is good for a couple creature comforts.
Along with this list of things, games and books are good to have to entertain the kiddies. It is a good idea to have things to occupy your time while you wait. You never know how long or short your wait might be when waiting for the power for be restored.