Whatever method you choose, you will need a good
supply of the appropriate fuel, the right grill, cooking pans that can
stand the heat and/or be disposable, and foods that can be cooked
in this fashion.
Charcoal and propane will take the oxygen out of your air, and this can be fatal quickly if you use them indoors. The only way you should ever even consider using these indoors is if there is a blizzard outside or you can't get outdoors at all for some reason. And then, you would have to be sure to open every door and window so that the air supply is constantly renewed. Even then use it only as long as necessary for cooking and keep the windows and doors open long afterward to be sure that there is enough oxygen indoors. It would be much safer to also stock up on firewood in advance or to just eat food that doesn't have to be cooked to be edible.
You may have to cook everything on your barbecue, so you may want to stock up on heavy-duty aluminum cooking items like caterers use. If you get enough, you can throw them out instead of washing them (or at least if food gets really stuck on them), and you can recycle the aluminum. Use your barbecue or firepit for double duty. When the meal is done cooking, the coals or wood will remain hot for a long time. Cook more food. Cooked food keeps longer than fresh, and you save on fuel. Or, put a large pot of water on the fire and heat it for bathing or after-dinner coffee or hot cocoa. Stock up on charcoal, lighter fluid, and matches, and you can use wood.
Remember not to bring the barbecue indoors or use charcoal indoors because it will remove all the oxygen, which can quickly become a lethal environment.
The fireplace is a good place for safely cooking if you use wood. For cooking over a wood fire in the fireplace or outdoors in a safe pit, you will need to find a sturdy grill. This could be propped up high enough with some bricks or large stones. A camping toaster over the fire does a decent job of toasting bread. Stock up on lots of wood for cooking, and newspaper and kindling for starting fires quickly. Long matches are the safest for use with the fireplace. The fire will burn hotter and stay lit better if you put the firewood up on a grate to allow for air to flow underneath. For the same reason, you need to move ashes out from underneath the grate occasionally. When there are so many ashes that you need to remove some, they should be put into a metal container which is kept far from any flammable item. The ashes will take several days, at least, to cool.
Camping stoves are available in lots of sizes and work great. They need propane. Try to estimate the number of meals you would need to cook on the camping stove so you can purchase enough containers of propane. And, remember that a propane stove should not be used indoors because its use robs the air of oxygen, possibly resulting in death.
One more method for cooking is the Dutch Oven. You can cook a good stew in the pot, and bake biscuits on top at the same time. A dutch oven can be used in the fireplace, in an open fire outdoors in a pit, or in the barbecue.
Evenly space coals underneath the dutch oven so the food won't burn on the bottom. A 12-inch pot would usually need 24 coals: for baking, put one-third of the coals under the oven and two-thirds on top; for roasting, put an even number of coals on top and bottom; and for stewing and simmering put two-thirds of the coals under the oven, and one-third on top. Save on fuel and time by cooking more than one food item in the pot at one time. Put vegetables and potatoes around meat in one dutch oven, cook chicken and rice together, or cook eggs right on top of hash browns. Beans can cook or bread or cake can bake in a second dutch oven on top of the first, with the coals on top of the bottom oven's lid acting as the bottom coals for the top oven.
Save on fuel and use sun's rays, even on the coldest day, with a Global Sun Oven solar oven. Even though it is called an oven, food can be boiled, steamed, roasted or baked at cooking temperatures of 360 degrees.