In order to cook well, I don't think you need to have a profusion of cookware, but the items you have should be of good quality - you will be surprised how big a difference it makes. From knives to pots to utensils, having the right kinds of tools will make your cooking easier and more enjoyable.
Buying items which are high quality means that they may be (relatively) expensive, and it may mean you have to build up your kitchen piece by piece, but it also means that those items you buy, if used properly, will last your whole lifetime, and potentially several other peoples' as well. For that reason, it is also worth looking for some items used, as you may be able to find well-made cookware that is still in great shape, for a fraction of the cost of buying it new.
Here is a little bit of a rundown of what items we use often in our kitchen. What exactly you need will depend on what exactly you plan to cook, and you will probably find that the more types of dishes you try, the more things seem to become "necessary", but I think this will give some good ideas as to what you might use certain things for.
Knives and other implements for cuttingStarting with knives, We have (all in stainless steel) a good 8 inch chef's knife
a good paring knife
and a good utility knife.
The chef's knife we use mostly for chopping - onions, potatoes, carrots - all that prep-work kind of stuff. It's also great for cutting meats if you need cubes of chicken breast or chunks of beef for stew, etc.
The paring knife is great for more detailed kinds of cutting, peeling or coring fruits, chopping smaller things like garlic or herbs, etc.
The utility knife we use for all kinds of things - it can be used for most of the above things as well, depending on your personal preference. it is also great for bread, tomatoes (anything where some ridges on the blade are useful), and having a nice wide knife like that, it is also good for spreading things like mayonnaise or mustard.
Knives are one of the best things to invest a little bit extra in, I think, as having high quality knives that will stay sharp and be able to be sharpened for a long time makes such a difference. There is so much chopping and cutting involved in cooking, and it is so much less tedious and time-consuming if you don't have the added hassle of dull knives that send vegetables flying, smash tomatoes to mush, squish bread, etc. Don't worry about cutting yourself, you are actually more likely to cut yourself with a dull knife that slips on whatever you are trying to cut.
We love our kitchen shears. I use ours a ton for poultry and fish, and it's just nice to have it around to cut twine, trim vegetables, cut up things which are already in a pot/pan, etc.
Pots, pans, and sheetsWhen talking about pots and pans, materials are quite important. Certain materials conduct heat better than others, certain ones may react with certain types of foods, and certain ones seem to have mysterious properties that help or hinder your cooking in different ways.
For pots and pans which you expect to use on the stove top, it is important to get ones with heavy bottoms, whichever material you use, as the heat distribution will be better. With thin-bottomed pots and pans, often the bottom of the pot/pan will get too hot too quickly, and it will be easy to burn your food.
Regarding materials, copper and aluminum conduct heat much better than cast iron or stainless steel, however, they can react with certain foods, and leave a metallic taste in them. Cast iron doesn't conduct heat as well as copper or aluminum, but it also retains heat better, so once it is hot, it will cook very evenly. The cooking surface of your pots and pans makes a difference as well - less porous surfaces will prevent foods from sticking in your pans, whereas surfaces like raw cast iron will have a tendency to really stick with things like eggs or fish, unless you use quite a bit of cooking fat/oil. Less porous surfaces, however, will not brown things like meat as well as more porous surfaces, so for browning meats, cast iron works very well.
We have a combination of a few of these things:
A good 10-12 inch enameled cast-iron skillet. This has a pretty rough enamel, so it is still a fairly rough surface, but doesn't require seasoning like raw cast-iron does, and is still very durable. It can be used in the oven or on the stovetop, so we often use it to brown meats/vegetables and then finish them in the oven. We also use it a lot for sauteing onions or other vegetables that will be added to a stew or soup or other dish.
A good 8-10 inch non-stick skillet. Ours is kind of high-tech, in that the inner core is aluminum, the outside is stainless steel, and then the cooking surface has a kind of glass enamel which is non-stick. Whichever one you get, it's important to get one where the non-stick surface is not going to start flaking off in your food like teflon will. We use this a lot for fish and eggs, since those are some of the most notorious stickers, and it's been wonderful. It also works really nicely for pancakes.
A small enameled cast iron skillet. Perfect for one or two eggs, a little bacon, or prep work sauteing something that will go into a larger dish.
A small enameled cast iron saucepan. Perfect for making sauces, gravy, heating stock to add to rice (as for a risotto or whatever). I think ours is about 5-6 inches in diameter.
A larger copper saucepan, lined with tin or nickel. As I mentioned, copper is reactive and can sometimes leave a metallic taste in some foods, so often copper pieces will be lined with either tin or nickel, which are non-reactive. This one is great for cooking grain or cous cous dishes, soups, drinks (spiced cider) and other prep-cooking as part of a larger dish. This can also be used in the oven or on the stove top, so it is very flexible in use. Ours is about 11-12 inches diameter, I believe.
A nice gratin pan. Ours is copper lined with nickel, there are also some really nice enameled cast iron ones. Besides actually making gratins, these are good for things like roasting poultry or other meats in the oven, and can be used on the stove top as well, so that you could then make a gravy or sauce from the meat drippings and pan juices directly in the roasting pan, once the meat has rested.
A cast iron dutch oven. We have nice enameled ones, very heavy, and we use them for all kinds of things, it is possibly our most-used piece of cookware. Soups, stews, rice or other grain dishes, it can also be used for browning/roasting meats and vegetables, and can be used both in the oven or on the stove top. We have a 6 1/2 quart and a 3 1/2 quart one.
A good stainless steel stockpot. Whenever (almost) we cook a whole chicken, we keep the bones and giblets and make a stock. Having a nice, big pot like this is the best way to do it, though you could make it in a dutch oven as well, though the amount you could make would be limited. We're wanting to buy some beef soup bones soon too and try out a beef stock. You can also use this for boiling anything that requires a lot of liquid - potatoes, pierogi or other dumplings, etc.
A good steel baking sheet. Good for baking bread or biscuits, roasting vegetables, baking cookies, etc.
Mixing bowls, rolling pins, mortar and pestle, measuring cups and spoonsWe use mixing bowls for all kinds of things, and we have some glass ones and some copper ones. The glass ones can be used for anything, and probably our most commonly used size is about 12 inches in diameter and about 8 inches tall. The main reason we have found to use a non-glass mixing bowl, is that whipping cream, and especially beating egg whites doesn't work nearly as well in a glass bowl as it does in steel or copper. Copper is the best, but is a bit expensive unless you can find them used (thankfully we did).
Rolling pin. I like a good, solid wood rolling pin. I'm not as big a fan of the ones with handles and a spindle that goes through the pin, I like the ones that are one solid piece better, but you just have to try them and see what you like.
A good mortar and pestle is a big plus, in my opinion. Dry spices keep better and are more flavorful if they are stored whole, and a mortar and pestle allow you to keep whole spices and then grind them up as you need to use them. You can keep a pretty small mortar and pestle just for doing that, so it's not too much of a space hog, and not all that expensive. Marble or a hard wood work well. You will be amazed at how differently spices taste when they are freshly ground as you are cooking. We also have a large marble one that we use for anything with liquid in it. Great for mashing garlic (for aioli, for instance), making pesto, curry pastes, etc. We use the hard wood one just for dry spices.
A good set of dry measuring cups and spoons in the standard increments, along with a 2 cup liquid measuring cup. With the spoons, one thing to take into account is if the spoons will fit into the containers you store your ingredients in. Having ones that are easy to level off and easy to tell when they are full is important as well.
UtensilsWe prefer almost exclusively wooden utensils as they weather well, withstand most cooking heats, don't mark or scratch up your pots and pans, and are really nice aesthetically. We have a number of spoons in different sizes, a slotted spoon, spatula, a couple of ladles, we just need to get some wooden tongs.
Oven dishesWe have a number of different glass dishes for baking things in the oven, in different shapes and sizes. We use them for things like macaroni and cheese, lasagna, casseroles and baked eggs.
TrinketsA bench knife. This is one of those things that is made specifically for use scraping dough off a counter or pastry stone, but we use it for all kinds of things - scooping up chopped onions, garlic or other veggies, clearing off the counter, etc. It's cheap and handy.
A vegetable peeler. This is another thing that is really simple, but makes a big difference if you get a good one. Thankfully, the good ones are still cheap. We've loved ones from Kuhn/Rikon and Swissmar. Make sure to get one that has the little thingy for digging out potato eyes.
cutting boards. again, we tend to prefer wooden ones, as we just like them aesthetically. we keep one small one for onion and garlic, a larger one for most veggies, and then a plastic one for meat. technically you wouldn't have to have separate ones for veggies and meat, but we do. it's up to you.
thermometer. handy for anything from checking to see if your meat is done to checking the water temperature for activating your dry active yeast before making your dough. we need to get a better one, but this one serves :)
A flour sifter. Good for certain baked goods where all your dry ingredients need to be mixed up well and have a tendency for clumping (like baking powder). I used ours most often for biscuit dough.
A colander. Made with one specific purpose in mind - draining things :) One of those things that you don't think is anything special, but we use it constantly. Pasta, veggies, cheese, anything that has liquid in it that needs to have it drained out.
So, those are some of our most commonly used kitchen items. It's been a process for us putting them all together, and some of those we've even gotten within this last week, but they are quality pieces, and things we will use over and over and over again for years to come, so it is worth the investment for us. If you have any questions or comments, just let us know. Bon Appetit! (and happy cooking!) :)