What You Need

You don't need a whole lot to start cooking. It's true! Here is a list of things you should stock your kitchen with.

A frying pan. I advise avoiding Teflon. There are great nonstick pans out there that are not Teflon, and some of them are great! I have an EarthChef skillet that is amazing. I got it for Christmas last year and it is in exactly as good shape as the day I bought it - unlike a lot of other pans I have had, it doesn't have gross build-up from burnt stuff. Everything just slides right off of it, which makes clean-up a breeze.
You want to avoid Teflon because it is carcinogenic and flakes off into your food after a while, which is obviously a pretty bad thing.
Never use metal utensils in your pan, especially if it is non-stick. Invest in some wooden spoons, which are seriously cheap, and really handy. I recommend a few, because I always lose mine, somehow.
A good-sized pot. Want to make pasta? You need a pot. Rice? Pot! Soup? Obviously, a pot. Come on, that's a silly question. Even if you're only cooking for yourself, don't get the tiniest pot, because it is really hard to cook pasta in a tiny pot. A 2-quart pan should do you pretty good, I think.
A chef's knife. A really good quality chef's knife is going to run you between $100 and $200. But don't worry! For your everyday use, you can get something pretty good for cheap. My first knife was an IKEA knife that cost me five dollars, and I used it solidly for three years with no problem, as long as you take care of it - I'll get to that in a later post.
The title of "chef's knife" is referring to the shape: it has a blade that curves upwards to allow you to chop without lifting your knife. The tapered point allows you to do more detailed work. While you can get away with just a chef's knife, a paring knife might be a good addition: paring knives are very small and are great for peeling vegetables, picking out bad things (like bruises or potato eyes), and lots of other things.
A cutting board. Look, I'm going to put it to you straight here. Your landlord does not appreciate cuts in the counter, and if you own your place, you're not going to like it either. Get yourself a cutting board! It doesn't have to be huge, just make sure it is large enough to have both hands comfortable on it - you don't want to be awkwardly balancing a vegetable off one end of the cutting board while you try to cut it. I recommend wood cutting boards (bamboo is pretty great), simply because I like the feel of them - but you can get plastic ones for very little money as well.
An oven-safe pan. A pyrex casserole dish, a metal cake pan, whatever. But once you discover the joy of roasting vegetables, you are going to want one! An eight-inch square pan is fine, but you can go up to 9x13 if you're feeling adventurous. I absolutely recommend checking out second-hand shops for pyrex or glass baking dishes. Almost every time I've gone to Value Village, I have seen at least a few. I got mine there for about four dollars and I use it all the time. These baking dishes are thick and heavy and sturdy-feeling, even though they're made of glass. They should be free of scratches and stuff stuck to them, but don't worry about staining, it won't hurt you.

That's it! Were you expecting the list to be longer? Because honestly, you can be up and cooking for less than a hundred dollars, easily. Once you get to more complicated things you might find that you need more - maybe a second frying pan, a vegetable peeler or even a food processor - but to start, to be able to feed yourself, this is all you really need.