(note: I didn't read all 66 posts since the opening post, though I did read warpus's)
I'm by no means a cookware enthusiast, but I cook fairly often and didn't spend a fortune on pots and pans - probably less than $150 total. And it's served me well.
My preferred materials are stainless steel and cast iron. Stainless steel is inexpensive and great for general-purpose cooking - most things you'd make on the stove for dinner do well in stainless steel. It's also pretty low-maintenance. It isn't the best at distributing heat evenly, but that doesn't always matter. I have 1, 2, 3.2, and 8 quart pots in stainless steel. The first three are my go-to cooking vessels, the last I use for larger recipes like chili. In retrospect, 1, 2, 4, and 6 would probably have been more ideal sizes. But you don't need everything under the rainbow - four sizes is probably sufficient, and maybe toss in an extra 1 or 2 quart one if you tend to cook several small things at once.
I also have one stainless steel skillet. But my other skillet is cast iron, and my griddle is cast iron. The big advantage for cast iron is that it's virtually non-stick. So if I make pancakes, I always make them on cast iron. Likewise for grilled cheese sandwiches. Both of them also benefit from the very even heat distribution that cast iron has, but stainless steel does not. For items like browning meat or sauteeing vegetables, I use the stainless steel, as it's lower maintenance and those don't stick enough to be an issue. Cast iron does have an advantage in that pretty much any cast iron skillet is oven safe, so you can also bake in it. I usually bake cornbread in my cast iron skillet, but it can be used for other items, too. I'd probably go with one large stainless steel skillet (12-inch probably, I think mine's 10, and it's a bit smaller than ideal for some dishes), a cast iron griddle of appropriate size for your preferred grilled foods, and optionally also a cast iron skillet. I've gone with the made-in-North-America-but-not-super-expensive Lodge Logic cast iron skillets, and they've done well so far. Target carries them in the U.S., among other stores (but if you buy at Target, I'd recommend not using a credit card).
I'm also skeptical of teflon, and haven't bought any myself. While it's generally recognized as safe, it's also documented that it isn't entirely safe when pushed outside of its recommended range. I like that I can preheat my cast iron griddle before making pancakes without worry, even if I forget about it and it gets really hot, whereas preheating teflon in a similar manner may degrade the teflon and be unhealthy. Between stainless steel and cast iron, I haven't missed teflon.
I wouldn't recommend buying a whole set at once. In part because it will likely cost more, but as importantly because it will take up more space and there will probably be at least a few pieces you end up using rarely if at all. Not that there isn't a place for more specialized pieces of cookware like double boilers. But you can buy that as you need it.
I don't know a whole lot about which brands are great. My relatively inexpensive cookware probably isn't as good as what my mom has had for 40+ years and that still looks great. But that was also more expensive, probably even before accounting for inflation. So you probably can get higher quality by spending more. But I don't know enough to recommend which brands are likely to be worth it, versus just more expensive because they're more prestigious.
