Buying the first set of pots and pans

Syrion has already provided some good advice, but I think I can expand it. Note: I live alone and cook for one. And there are a few pieces I use every time. I have more, but I only use them when the primary tool for a task is busy because I am making an involved recipe consisting of multiple components. Beginning cooks seldom make such recipes. So here the list of the minimal setup which will get you through most cooking.

1. Pans The minimum is one ceramic coated pan. They are non-stick and can be heated to 400°C, so they are usable for everything you'll fry. The downside is that they are expensive and lose their non-stickiness over time. So you might want to go with two pans: one standard non-stick (PTFE) for eggs (can't be heated too much) and one normal pan for everything else - cast iron if you are willing to take care of it, else stainless steel. Invest in the thickest bottom you can find, 8 mm is a good starting point. As for size, I don't see why you'd need a big pan if you cook small amounts, my primary pan is 8 inch.
2. Pots Don't buy any. Buy an enameled dutch oven for everything you will boil and simmer. If you live in the USA, you can get a decent size for $50, in Europe the situation is worse, only the expensive brand name stuff is available. An OK size for a single household is 3 liters. If you find yourself often cooking dishes which need two pots (e.g. pasta with a cooked sauce), get additionally a deep sauce pan, SS needs the least maintenance. Again, look for a thick bottom.
3. Oven pan It is for casseroles, roasts, moussakas, lasagnes etc. You can also bake in it - savory things like quiches and filled breads, but also sweet pastries, pies and cake layers. Round is the most versatile shape. A size around 22 to 26 cm diameter and 4-5 cm depth is good for almost everything. As for the material, I prefer porcelain, it ensures a slower, more even baking. It can also be used in the microwave. If you get metal, you can first brown your onions and meat in it in stovetop, then add the veggies and shove it into the oven.
4. Pizza stone A good investment even if you only bake frozen pizza. Great if you ever start making your own pizza and bread. Look out for a massive one, not the thin stuff you get for nothing.
5. Bowls Two are the minimum I've been able to live on. A smaller one which fits on the dutch oven, preferably glass, can also be used as a double boiler. It is also good for whipping small amounts of yolks, cream, etc. You can make 1-2 portions of salad in it. The bigger one is for doughs and batters, but also for salads. If you add a third very small one (3-4 inch rim diameter), you can whip small things even better, but also eat soup out of it, serve nuts and gummi bears to guests, etc.
6. Strainer Very important. It is used for such basic recipes as pasta, stock, etc. You can also wash fruit, veggies and leafy greens in it. Get one which can be hanged over your sink. You can also buy a colander for pasta and washing, but if you only get one of them, it should be the strainer.

If you don't bake, that's about it. If you bake, add a springform pan, muffin cups, a silicon mat and a piping bag with tips. (I assume that your oven came with a cookie sheet). You'll also need 2 knives (chef's and a small one), a cutting board (wood, bamboo or plastic, anything harder blunts your knives) and some things to stir/serve with (ladles, sauce spoon, big spoons, tongs, etc). I consider a digital scale and thermometers also essential for a kitchen, but many people go by without them. You're then set up for cooking in a minimal kitchen.

If you can get what I listed above as a set, go ahead and buy it. I have never seen such a set, so I think it is better to buy them separately. Later, if you notice that you miss something, you can always buy it as a separate piece.