get started with:
chef's knife
A chef’s knife is probably the most important kitchen utensil. It doesn’t have to be fancy or pricey – an inexpensive $30 knife with an 8 to 9 inch blade will suffice. Just keep it sharp. By sharp, I don't mean use a honing steel, I mean take it to a knife store and get it sharpened often, or learn how to use sharpening stones. Choose a knife that feels comfortable in your hand. This R.H. Forschner by Victorinox is a good basic one. When the time comes to upgrade visit Korin.
stock pot
A stock pot is important to have on hand for boiling pasta, making stock, blanching string beans, simmering risotto or cooking a lobster. A stock pot can do small as well as large tasks. A sturdy, heavy stainless steel-lined pot with aluminum core, like this All-Clad, will heat up quickly and evenly and should last years. Less expensive ones, like this, work well too.
wooden spoon
A true do-all. Good for the frying pan, good for mixing thick batters, and you can use the handle as a cocktail muddler. Don't put it in the dishwasher, and wipe it from time to time with mineral oil. Avoid those spindly ones that can snap when stirring thick polenta. A spoon carved from strong cherry or olive wood that can be bought at most cooking supply stores will last through the years.
whisk
While a basic whisk will do most jobs, try to find one with stiff wires (like the Exoglass handle ones from Matfer) to help you thicken meringues and emulsify dressings.
mixing bowl(s)
Try to avoid plastic or melamine. Stainless steel or glass is better, because they aren't as difficult to keep completely clean, and they don't absorb oils or odors. Stacking bowls are helpful for storage in a small kitchen. Some, like these Sori Yanagi bowls, come with strainers that fit seamlessly inside. Mixing bowls don't need to be chic or expensive. These inexpensive glass ones are good basic bowls.
large skillet / fry pan
Cast iron is a good place to start. Say, ten or twelve inches. They are cheap. They are an excellent conductor of heat and great for cooking everything from a steak to scallops to eggs. After you use them, wash them quickly by hand, dry with a towel, reheat over the stovetop to evaporate all the water molecules stuck to the pan, and fill the pan's pores with a thin layer of vegetable oil. If you leave them to soak in water, they will rust. If cleaning a cast iron scares you, go with a basic stainless steel pan, stainless steel coating over an aluminum core, like this one from All-clad.
tongs
In restaurant kitchens, tongs are a chef’s third hand. At home, cooks will find them equally useful for picking up hot baking sheets or reaming a lemon. Look for sturdy tongs with a grip handle, such as these Oxo tongs.
cutting board
If you can take care of things, get a maple one, maybe from John Boos. Oil it often, don't soak it, don't put it in the dishwasher. Do enjoy it.
a pepper mill
For some reason French maker Peugeot seems to be the undisputed champion of this category, but I have yet to meet a pepper mill from any maker that didn't actually grind pepper.
microplane zester / grater
A good grater is important when working with hard cheeses, citrus rinds and nutmeg. In 1994, when a homemaker picked up her husband’s woodworking utensil to zest an orange peel, the Microplane took on a new guise — that of a kitchen grater. This great American contribution to the kitchen slides into the thinnest of spaces. They make excellent gifts for Europeans, as they are both sparce and pricey in Europe.
paring knife
Many tasks, like hulling strawberries or coring apples, cannot easily be done using a large knife. That’s when a 3-inch paring knife comes in handy. Like the chef’s knife, it doesn’t have to be fancy – just sharp.
swiss peeler
Swiss peelers, like this Kuhn Rikon, are cheap and can peel a thick-skinned squash just as well as a carrot. They are great for cutting zucchini and asparagus into ribbons for salads or pastas.
and more advanced:
meat thermometer
If you cook a lot of meat, then a thermometer, digital or dial, is indispensible for achieving a certain temperature. I’m more comfortable serving a roast chicken that I know has reached 165 degrees. Remember to calibrate thermometers to either 0 degrees in ice cold water or 212 in boiling water. Or, if you cook meat often, you may want to invest in the speedy and accurate Thermapen. With a range of -50 to 572 degrees Fahrenheit, it serves as both a meat and candy thermometer. Best of all, it doesn’t require calibrating.
bench scraper
For cleaning up, for cutting doughs.
dutch oven
For braised dishes in the oven. Both Le Creuset and Staub make gorgeous, functional ones.
squirt bottle
For storing and pouring salad dressings. Available at most kitchen supply stores.
scale
For more serious cooks and bakers, a scale is invaluable for a few reasons: 1). most proteins are measured by weight, and 2). for better accuracy and less mess, many bakers use scales rather than measuring cups. As a result, many baking books measure recipes by weight. The KD-700 Professional by My Weigh, is incredibly precise and easy to use.
plastic wrap
No other plastic wraps work like Stretch-tite. Once hooked, the Wrapmaster will be your next guilty pleasure.
more than that?
. . . and you're on your own. You have probably done enough cooking that you know you might like another saucepan, a specialty baking pan, a salad spinner, or a particular appliance.