I've been in the kitchen a looong time -- from the time I could reach the counter on a step-stool, Mom put me to work stirring, measuring, rolling, mixing, and peeling. I still hate peeling. Anyway. In all that time, I've learned that there are some things that you really need, and a whole lot of things you really do NOT need.
Here are my absolute essentials. In other words, these are things you'd find it pretty tough to cook extensively at home without:
two knives -- one 8 or 10 inch chef's knife and one small paring knife. There's almost nothing you can't cut with these two. Knife sets are a HUGE rip-off -- you can get a good chef's knife for $30-40, and a paring knife for $5, and that's absolutely all you need. Buy your knives (both of 'em!) individually from a place where you can actually hold them and see if they fit your hands and feel comfortable. And keep them sharp. Repeat after me: "A sharp knife is a safe knife!" You can use the bottom of a coffee mug to hone your blades. Then a couple times a year, take them to a cutler and have them professionally sharpened. It should only set you back a few bucks per blade. If you have funds for a third knife, make it a good serrated knife, which will serve you well for bread, chicken carving, tomatoes, and anything delicate.
two or three cooking pots -- 1) a large dutch oven or oven-safe stock pot for soups, making stock, boiling pasta, doing braises, etc. The heavier the better. 2) A 10-12 inch skillet with a heavy base, nonstick or not, cast iron if you can find one. This you'll use for browning, stir-fries, sauteing, making sauces, and on and on. It's your everyday pan. Get an oven-safe one if you can. 3) A 3-4 quart saucepan, again with a heavy base. Useful for steaming veggies, cooking short pasta, making sauces, etc.
a few baking items -- a couple of bread pans, a 9"x12" glass or porcelain baking dish, a muffin tin, and one or two sturdy half-sheet pans, which are DIRT CHEAP at Sam's Club, Costco, and restaurant supply stores.
a few (FEW!!) utensils -- a couple of wooden spoons, a whisk, a pancake turner/flipper thing, a garlic press, a vegetable peeler, a bottle opener, a can opener, a rubber spatula, kitchen shears, and a pair of tongs. I cannot live without my tongs -- they're by far the most versatile utensil in my kitchen.
some miscellaneous stuff -- a medium-sized and a large mixing bowl, a couple of big cutting boards (one for raw meat, one for everything else), a good set of measuring cups and spoons (or a scale), and a big glass liquid measuring cup.
In the "maybe" or "when you have the money" category:
a roasting pan. I got one for $20.
a meat thermometer
an oven timer
a square baking dish
an electric kettle (this is an essential for me as a tea drinker, and it has lots of other uses, but for most Americans it's not really crucial)
an electric hand mixer or a stand mixer (like a KitchenAid)
a food processor
In the "heck no, what are you thinking" category:
anything from an infomercial
knife sets (see above)
anything that only does one thing (a "unitasker") like mango slicers, avocado forks and other absurd drawer-space-wasters.
Next up: stocking that pantry!