:hi:
Okay, lemme start by saying I'll likely echo some earlier ideas, upthread ......
Cookbooks: The best all around cookbook has already been named - Irma (et al) Rombauer's
The Joy of Cooking. If you get only one cookbook all your life, this should be the one. They touch on every aspect of cooking and best of all their recipes work! The book also has lots of good tips and techniques.
Microwave oven: Get one. For a single person kitchen, I'd think the smallest one will do. This could well be a yard sale item.
Tools: I'd suggest strongly you save up your bucks and bum a ride to one of the big box stores. Target is good. So are Linens and Things and Bed, Bath & Beyond (Reason). This will be your source for tools. I'd suggest you avoid yard sale items for these ... you just never know ....
Anyway .... here's a good idea for a starter set of useful tools:
An assortment of wooden utensils. They often seem to be sold in sets. As long as it has two sizes of spoons, that's probably the best bet. Recently they've started selling brightly colored plastic (nylon?) substitutes for wooden spoons. These are actually an improvement, so maybe get these instead.
A colander. Metal is better than plastic. In fact, avoid plastic. (Funny thing about plastic in general .... it is chemically *very* close to oil and grease and always seems to have a greasy feel to it. I find it sorta 'icky' to use for some things .... like colanders.) If you find a metal colander at a yard sale, and it looks clean, that's okay, too. You want one that is large. 10" to 12" across at the top.
Wire whisk/whip. Get a smallish one ... maybe 8" long. Metal only. No plastic (see above).
Spatula. Technically, these are called 'turners'. You want one for general use. Stiff plastic is okay, but make sure it won't melt in a hot pan (some definitely will!). They make these in a bazillion shapes and sizes. I suggest one with a solid blade and one with a blade with slots or holes in it.
Rubber scraper. The best ones are made of silicone and are very heat resistant. Get one or two of them. They are available in many sizes.
Kitchen fork. This is a large fork for use when lifting heavy items like a steak or a whole chicken. Go for the most heavy duty one you can afford.
Pot holder and/or oven mitt
Knives: As has been said already, get the best you can afford. Cheap knives, quite simply, are dangerous. That is NOT hyperbole, either. Trying to cut with a dull or bad knife causes you to apply extra pressure. Extra pressure causes things to slip. Slipped knives are far more prone to cut or stab the user. Even a dull knife can go right through your hand. GET GOOD KNIVES. Wusthoff and Henkels are excellent brands who have recently started selling knives made in China. Not as good as their top line products, they are still quite serviceable. I'd suggest three to start.
A Santoku knife is all the rage these days, and for good reason. They're modeled on an Asian design and have good balance. They're smaller than a Chef's knife and therefore less intimidating and more forgiving for a novice. You can find the ones made in China for as low as $15.
An alternative to the Santoku is the classic Chef's knife or French knife. If you choose this, get one that is 8" or 10" long. Try to stick with a name brand. And NO serrated edges. Get one that can be sharpened. It will have an edge just like the one on the Santoku.
Get a slicer/utility knife. Same comments as for the chef's knife. A 6" ot 8" blade will do nicely.
Lastly, get a paring knife. One that looks like a small version of the utility knife is perfect. A 3" or 4" blade is fine.
Pots and Pans: Yard sales are okay for these. As has been said, think twice about Teflon (health issues) .... although, to be fair, if you don't overheat it, you can probably do just fine. But not around birds. Teflon's off-gas will, literally, kill them. Also, for Teflon, I'd only buy new. You'll only need one ..... an 8" frying pan.
Cast iron is great. Search the archives of this forum for tips on the seasoning and care of cast iron. We've discussed that a lot in the past. Consider a 6" and a 10" frying pan. You may also find that a set, as shown below, is pretty cheap to buy new. No need to worry about brand names. While there are brand names, cast iron is pretty much all the same ....... except for the new 'pre-seasoned' stuff. No need to go for that. Seasoning one is easy.
You'll also want a 2 qt and a 4 qt soup pot.
Get an 8 qt pot. You'll use this for soup .... and most importantly, for pasta. These come in two varieties .... those that are wider than they are tall and those that are taller than they are wider. You want the taller one. (The shorter ones are called 'dutch ovens'.)
A word about cookware ...... heavier is better. Those paper thin ones they sell at the grocery store are a false economy. They give you no heat attenuation. In use, you'll burn stuff more often than not and never know why you burned it. It wasn't you. It was that cheap damned pot! The most economical is aluminum. You might also consider enamel on steel. Stainless steel is great, but costly. Also think about eBay. There's lots of Revereware on there, and generally, it will last two lifetimes. As common as it is, used is commonly available and not too costly. It also turns up at yard sales. You'll know it because it has that copper bottom and distinctive handle ... like this one:
Wow .... this has gone a while and I'm losing my train of thought. I may post more later.
And all of this is in addition to what's been posted above. It is all good advice.