I can't tell you how important a pair of tongs is, whatever style you like. Trying to turn a hot piece of meat over in hot oil with a fork or a spatula is hazardous. The meat can plop over, splatter hot oil, and you might find yourself with a lovely red beauty mark. Tongs.
Wooden Spoons, or other "cooking" spoons
I have several of these. My wooden spoons are actually made of bamboo. I find that bamboo is very durable. These will last for years and years. The great thing about wood or bamboo, is that the material does not conduct heat. You can leave it sitting in the pan for a few minutes, and you aren't going to burn your hand when you reach for it again.
I would recommend having 2 or 3 spatulas in different sizes. A spatula should be thin, but strong. If it is too thick, you can't slide it under delicate foods. If it isn't strong, your food will fall off a drooping spatula. My large metal one is great for serving a honking chunk of lasagna. My little metal one is perfect for getting brownies out of a pan.
A Slotted Spoon
A slotted spoon is exactly what it sounds like. A large serving spoon, with slots or holes in it. Sometimes you need to scoop up food but not the liquid it is in. That's what this is for.
A ladle is like a little bowl on a handle. If is for scooping liquids and solids, like stews.
A Colander, or strainer, is used for....straining. I personally like metal ones, because they can double as a steamer basket in a dutch oven.
Now on to the cookware.
A Frying Pan or Skillet
Skillets are wide and shallow, and designed for sauteing, frying, browning foods. I would recommend having a large and small one. Whatever style you like. Cast iron, stainless steel, non-stick. Your choice.
Saucepans are cooking pots, not just for sauces. The most commonly used sizes, seem to be 3 quart and 2 quart. Most have long handles.
A Dutch Oven
A Dutch oven is like a large saucepan, without a long handle. They are ideal for cooking large quantities, soups, stews, etc. They are normally about 6 quarts in size. They are used for cooking or baking. You've seen my blue one quite a bit. I love the blue one, because it is enameled cast iron, and can go from the stove top, straight to the oven. Because it is cast iron, it also heats steadily and evenly, without hot spots or scorching of the food. Enameled cast iron is also safe for a glass-top stove. Simply pick it up when you move it, and don't slide it across the surface. Traditional Dutch ovens are made for baking, and have lots of detail and information that I couldn't possibly include in this post. Maybe for a future post.
A Stock Pot
Now this is a stock pot. It is very similar to a Dutch oven, but is larger and taller. Many cookware sets come with one. I don't use this as often as I do the Dutch oven, but its size is perfect for making stock/broth, and for cooking long pasta like spaghetti or fettuccine, because the noodles fit into it without breaking.
Now on to the bakeware.
Bakeware comes in every shape and size imaginable. There are kinds that are very multi-purpose, as well as kinds that have special purposes.
Some of the basic baking dishes, are cake pans, pie plates, and muffin pans. Basic cake pans can be round, square, rectangle. I would recommend having a 9x13 inch and a smaller 9 inch square or round pan. Those two can handle most of your baking needs, not just for cakes, but for many other things, like lasagna and everything else. Also, a 12 cup muffin pan and a pie plate/dish.
A few specialty cake pans, that I don't think are necessities, but are very common, are a spring form pan. A spring form pan is a two-piece cake pan. The side unlatches and removes from the base, leaving the dish intact. This is perfect for delicate things like cheesecake. Things that you would remove from your pan, but don't want to turn up-side-down to do so.
Another specialty pan is a Bundt Pan. These pans contain the same amount of cake batter as a 9x13 but are so pretty.
Loaf Pans are designed for baking loaves. Whether it's a loaf of pumpkin bread or a meatloaf. They are much like a cake pan, but are a little taller, and normally 9 inches long and 4 - 5 inches wide.
A Cookie/Baking Sheet or Stone
A cookie sheet or stone is designed for baking items, open to the heat of the oven. Some are flat, some have a lip around the edge. I like my stoneware ones, but many prefer metal ones. I think stoneware heats more evenly, but it takes a little longer to warm up that metal. For instance, when baking a batch of cookies, the first pan will take longer, allowing for the stone to heat up. Whatever your choice.
A Bar pan is very similar to a cookie/baking sheet, but the bar pan has a definite side to it, about 1 inch tall. Bar pans are commonly about 10 x 15 inches. They can do double duty as baking sheets too. If you only have one, this will do the job of both. You can also bake messy things on one, and the side will keep the liquids from spilling over onto your oven floor.
A Roasting Pan
A roasting pan is a baking pan that has a rack inside it to lift the food off the floor of the pan. They are idea for cooking things like chicken, ham, turkey, etc. It allows the fats of the meat to drip off, and not pool around the meat. These come in many styles; rectangle, oval, lids or no lids. Some don't have racks, but have little mounds in the floor that serve the same purpose, creating a space for the fats to pool under the meat.
And last but not least...
Have several, and keep them handy. I have had these potholders for years and years. They should be thick, but not too thick. You want them to insulate your hand, but be flexible enough to wrap around the handle of a pot you are trying to grab.
Printable List: Kitchen Essentials