Your stove top is not a campfire, you can’t just hold food over the fire until it’s done. You need pots and pans. Like with all kitchenware there are seemingly limitless variations and specializations when it comes to pots and pans, but I’m a generalist and if you don’t want to spend a lot of money you should be too.
SKILLET: This is your work horse. nearly all general purpose heat related violence will happen in a skillet. Egg frying? Check. Caramelizing onions? Check. Stir-fry? Pancakes? Bacon? Triple-fucking-check. I like a 9-12 inch skillet with a lid. An active piece of cookware like a skillet is where you’re going to need to really consider material composition. Stainless steel and aluminum are both cheap but steel is going to last you longer and won’t react with your food, if you’re willing to spend a little extra cash you can buy anodized aluminum or a steel pan with a copper core. When it comes to non-stick I think it’s more trouble than it’s worth, you have to baby the pan and you can’t get it hot enough for a really good sear without damaging it. Personally, I use an enameled cast iron skillet. As long as I don’t drop it, I’ll have this pan for at least a decade. However if I do break it, this pan cost about nineteen dollars at a supermarket, so, not the end of the world.
SAUCEPAN: A saucepan is a small pot with a single handle. The name is pretty self-explanatory. You will use this pan for everything that would otherwise slosh out of your skillet, but does not warrant a stockpot. With a saucepan you really want to be able to control the heat, so something with a high degree of thermal conductivity and even heat transfer would be great right? Unfortunately the best material would be copper, if it wasn’t slightly cheaper than a gold toilet seat and almost as useful. I hate to keep beating a dead horse but copper is just too reactive for a wide array of cuisines. In this case I would suggest an anodized aluminum saucepan, not the non-stick variety mind you, just the regular kind. I want to be upfront, an anodized pan cannot go in your dishwasher, that will ruin the finish and like so many things in life, the finish is everything.
STOCKPOT: What is a stockpot for? Soup or stew mostly, I mean if you really needed to you could make a stock I guess. Stockpots are also good for cooking rice, boiling potatoes, and all other sorts of wet stuff. When it comes to stockpots you want to avoid reactivity like the plague. You will be cooking food over a long period of time in a stockpot, if it is reactive it will react a lot. A stock pot will also have plenty of time to heat up and even out, so you don’t need to worry about great thermal conductivity. I would suggest getting something made of stainless steel, the most durable, cheapest option, or enameled cast iron which will require a gentler touch.