I figure I have three primary groups who are interested in Cooking for Two. One group is the so-called empty-nesters. They're older couples whose children have left home and they're trying to adapt to cooking less food. Even though they may be accomplished cooks, adjusting to cooking for two after cooking for four or six isn't as easy as it seems. The next group is childless gay/lesbian couples. This demographic is probably where most of my middle-aged readers come from. They may also be accomplished cooks, already familiar with cooking for two, and just looking for great recipes.
The last group is young couples who don't yet have children. They may be accomplished cooks, but probably aren't. I probably don’t devote enough attention to this last group because it's been so long since I've been there (I started learning to cook 50 years ago when I was six). But I have enough young people in my classes to understand what you folks face and thought it was time to specifically help you out. So here's what a basic kitchen needs.
There are two ways of approaching outfitting a kitchen: go cheap and, essentially, disposable, or expensive and commit to taking care of the tools. Sometimes one way is better than another, but in general if you’re a beginning cook, not. But keep in mind that although you don’t always get what you pay for, you almost never get what you don't pay for.
Knives
According to an article I once read, there are two kinds of chefs: those who love pots and those who love knives. You can tell which you are by what kitchen tool you would grab when escaping a burning building. In my case I'd grab my cat and my Spanish chef's knife - neither of those can be replaced. The knife was a gift from my parents after their first trip to Spain and that they returned with such an excellent blade was purely an accident. And short of a trip to Spain, you can't get one of these.
Although more is better, you absolutely need two knives. Requirement one is a chef's knife (compare prices). A chef's knife has a 7 to 12 inch curved blade. It is not serrated. Serrated knives have their uses such as cutting bread or soft fruit and vegetables (when you don't keep your knives as sharp as you should). A stamped knife blade is cheaper (and should be regarded as throw-away) a forged blade is far better. The stamped blade will cost $25 and the forged blade $70 - $100.
You also need a 3 - 4 inch pairing knife (compare prices) for fine work (personally I seldom use my paring knife - but I know chefs who absolutely rely on theirs). Same deal as above, a stamped blade is a throw-away that costs $5 - $8. A forged blade will be $25 - $30.
Most of my knives are Wusthoff (German, forged stainless steel). They cost a lot but will last longer than I will. I also have two of the Spanish blades now (the second is a monstrous 12-inch chef's knife - almost a sword), a couple of Gerber knives, and the first knives I bought, Sabatier high-carbon steel.
Other useful blades include a serrated bread knife (which saws through crusty bread instead of crushing it), a 6-inch utility knife, and a 6-inch Santoku blade.
Don't bother with buying high quality knives if you aren't going to keep them sharp. This means sharpening the blades about every six months (I use a Chantry knife sharpener) and a "sharpening" steel - which doesn't actually sharpen but instead straightens the blade's edge. The steel should be used every time you pull out a knife to use it. Try several blades out in your hand to see which feels best to you.
Pots and Pans
I'm in the minority among chefs, but I recommend buying a set. This way all your pots and skillets will have the same cooking characteristics, which I think makes life easier on a beginning cook. With one exception, it doesn't really matter if most of your pots and pans have stainless steel interiors or Teflon. But you want to have at least one 10-inch Teflon skillet and one 10-inch stainless skillet and lid(s). The Teflon is for eggs, omelets, fish, and other delicate foods. The stainless is for browning meats when you want to make a pan sauce.
You'll also want one-quart, two-quart, and four- to five-quart covered pots. Again you can go cheap or expensive. I have a set of Cuisinart pots and pans, all stainless and a cheaper Wearever Teflon-coated skillet (compare prices). As with my knives, the pots will outlast me except for the non-stick skillet. But Teflon wears out in five to eight years anyway so get a cheap, but heavy one.
I have other pots and pans including an ancient cast-iron skillet that was the first pan I ever bought and I love. But the three pots and two pans listed above are all you really need.