Here's just a few of my favorite tools in the kitchen: Iron pans, heavy-bottomed saucepans, stainless steel pots, a pressure cooker, and a cleaver.
Iron frying pans are awesome. I cook everything I can in them. The iron heats uniformly, it retains heat well, and is thick enough to not let foods burn easily. I even roast chickens in the oven in my frying pan, as other roasting pans are much harder to clean up. Season a brand new pan by rubbing olive oil on it, leaving it in the oven on extra low heat for a day or so. "Seasoning" it is really no great, mysterious feat, as even just starting to cook with it will also season it. But by seasoning it, it will clean up most effortlessly.

Another tool is a heavy-bottomed sauce pan. I've seen and tried many of the latest in cookware over the years, but I'm not impressed. On occasions where a saucepan is needed, a heavy-bottomed pan is invaluable. Look for stainless steel, with a thick bottom, layered with extra metal (such as copper). If you're preparing something time consuming, you don't want to waste more time throwing something burnt away, having to clean up the pan besides. A good saucepan is worth the investment.

When cooking pasta, potatoes, beans, etc., a stainless steel pot is great. With all the water
in the pot, burning is not a concern, so you don't really need a fancy-bottomed pot. A basic
stainless steel pot will do the job and will clean up much better than aluminum.

A pressure cooker is also handy. Stainless steel will be a bit pricier than aluminum, but it is worth it. There is some health concern when using aluminum; it's been suggested that a trace exposure to aluminum might occur. But, stainless steel or aluminum, bottom line is: A pressure cooker cooks foods quickly and efficiently at a lower heat. The pressure keeps the heat in, allowing extra hot temperatures to be reached. Ideal for making chicken stock or for cooking brown rice or beans, the pressure cooker is a wonderful tool to have.

A combination blender/processor is also great to have. The competition has finally come up with something that's the best of both worlds, and it even saves you cupboard space by being two machines in one: The Oster brand blender with food processor attachment can be the answer for many cooks looking for one machine that can do it all. Or at least, can do more than an old-fashioned blender. I highly recommend the combo-blender/food processor for friends who like to cook, but don't want to invest in the pricier processors.

This Really Makes the Cut

A good knife works wonders. If you have a favorite knife, you know what I mean. Most everyone at the deli has concurred that a cleaver is invaluable in most any vegetable-prep situation and in slicing meats thinly after cooking. Such knives are found for a very reasonable price in many Asian grocery stores. Look for one with a thin, stainless steel blade, sized right for your grip. (If the knife is too large in your hand, using it could prove awkward.) Safety is another feature. You can learn to guide the knife with one hand, chopping with the other, curling the fingers of your guiding hand, keeping them clear of the knife. Keep your knife sharp with a sharpening blade and it will serve you well.