Chef's knife. A weighty blade for chopping or slicing.
Serated knife. To use with slicing bread and tomatoes. Worth the investment.
Carving knife. A thin flexible blade for accurate carving.
Pots and pans
Skillet (25cm), with a long handle and sloping sides
Saucepans, 1 and 1.5 litre, with tight fitting lids
Saute pan, (25cm), straight sided, heavy-bottomed pan
A large stock pot for making soups and stews
Blender, inexpensive, purees everything from milkshakes to soup
Electric mixer, heavy duty
Hand held mixer
Colander, for draining and straining
Cutting board. Best to get one board for meats and another for fruit and vegetables, otherwise always be careful to use one side for meats and the other for fruits and vegetables.
Rasp, metal carpenter's tool for finer grating and zesting
Turner or flipper, metal or coated, solid or slotted
Measuring cups for dry ingredients
Measuring cups for liquids
Mixing bowls, glass, small, medium and large
Spatulas, rubber and heat resistant, small and large
Spoons, wooden, for mixing and stirring
Spoons, metal, slotted and plain, for stirring and serving
Whisks, small, medium and balloon, for sauces, beating eggs, whipping cream
Mixing bowls (You can get them in stainless steel, ceramic or glass. I prefer glass but they are all good. I don't think you can ever have too many mixing bowls and I like them in different sizes, from small to big. You can usually find find sets that fit into one another for easy storage.)
Round cake pan (own choice) - I have two.
muffin tins - small and large (good enough for cupcakes)
Cake or baking dish (own choice)
Pans come in aluminum, non-stick metal and glass and are all good. Use non-stick for your muffin tins and cake pans but avoid them for pie plates since the non-stick surface will get scratched when you cut the pies. Generally speaking the heavier the pan the better it is.
2 baking sheets with or without rims. Make sure they are solid enough not to bend when you hold them.
Other baking essentials
Set of dry measuring cups
2 wire cake racks
Cookie cutters - various shapes and sizes
Toothpicks for testing doneness of baked goods
Cleanup and storage
Plastic containers with lids for storing leftovers
With the above in your kitchen you should be able to handle most baking recipes with ease.