If you cook for yourself a reasonable amount then I think you need three different kinds of frying pan. I have six frying pans, only because I have two sizes of each type. They can be remarkably inexpensive. Or, you can spend a fortune, but I’m not sure it will make any difference to your end result.
I own three kinds of frying pan, cast iron, non-stick, stainless steel. Here’s what I use them for and this will explain why I have three types. The duplicates for size is for larger and smaller quantities, fairly self-explanatory. I use all three frying pan types very regularly depending on what I am cooking.
I’ve had this pan for about twenty years. I bought it from the back of one of those old style ironmonger and hardware stores you just don’t seem to get any longer. It cost me £10. It has a thick gauge and a good heavy base. This makes it heavy to lift. But it holds a lot of heat and is fabulous for cooking things that need a good hot pan, typically steaks or searing a joint of meat, or pan frying a fish to get a nice crisp skin. Like all cast iron pans, you must look after it. It needs to be seasoned before first using, which is basically just burning a film of oil onto the pan with as much heat as you can muster (like putting it in your oven turned up to the maximum.) After seasoning, it builds up a non-stick coating.
A well-seasoned pan can easily cook things like fried eggs with no sticking. Always wash your cast iron frying pan with hot water only. This maintains the slightly oily non-stick effect. In practice, I find washing the frying pan is very easy. Putting it in the dishwasher, or using detergent, would ruin it and you would need to start seasoning it again. It’s also unsuitable for cooking liquid type sauces that would degrade the coating. A tomato sauce will cause the seasoning to be degraded because it is quite acidic. That’s why I have a stainless steel pan.
This is the pan I turn to for cooking things that have sauces that will otherwise degrade the seasoning on my cast iron pan, eg. tomato-based sauces. I cook all my wet sauces in this pan. The pan has a good heavy base and also a lid. It works really well when softening onions, or making a soffrito. I can safely put this pan in the dishwasher and it saves a lot of effort. I know that some people will season these and you can get them fairly non-stick. But if it’s non-stick I need I either use my non-stick pan or my cast iron pan.
I think everybody needs a non-stick frying pan. It’s not something I use all the time but, for those essentials, like an omelette, they are indispensable. I have two sizes and I usually cook my fried eggs in them too. Anything that might stick a bit to my cast iron pan, like a skinless wet fish fillet, get’s the non-stick treatment. If you use wooden or plastic utensils, and don’t overheat the pan, the non-stick coating lasts a while.
My other strategy is to buy a medium quality pan. The really cheap pans often lose their coating very quickly and then they are only fit for recycling. Equally, I think that some of the very expensive pans don’t really last much longer than the medium quality pans. So my approach is to buy a reasonably durable medium priced pan and be prepared to simply replace them when they start to fail every few years. The fact that they just slot into the dishwasher nicely is another virtue.