Le Creuset enameled cast iron dutch oven and lodge cast iron skillet are my go to for most things. These and full clad stainless will last forever. If you go non-stick, get bargain basement and replace every year or so. Non-stick just doesn't last regardless of quality.

I've had good experiences with carbon steel pans as a long lasting replacement for what you would use nonstick for. They are similar to cast iron in that you season it, but the metal is smooth rather than rough, making food less likely to stick right out of the box. It is also lighter than cast iron.

However, carbon steel (and cast iron for that matter) will never truly be "nonstick". I prefer the term "stick resistant". With the right cooking technique, I think this doesn't matter though. In fact, I have been able to fry eggs (a food notorious for sticking badly) in stainless without a hitch. The main things I do to keep eggs from sticking is a) Preheat before cooking (I use 3/10 on my electric stove), b) Use some sort of fat (butter, bacon grease, etc), c) Wait until the white has mostly set before moving the egg around, and d) Use a thin metal spatula to release foods from the pan easier. This technique should NOT be applied to nonstick though, as toxic fumes can be emitted from overheated Teflon coatings. You also need to be careful to not preheat too hot or too long, as your pan may warp.

There is also the maintenance aspect of it. Be prepared to hand clean only, as putting carbon steel or cast iron in the dishwasher can make it rusty. Rust can be fixed, but it is best to avoid it of course. Unlike what many say online, you can use dish soap to clean it, it won't damage the seasoning. What will damage the seasoning is heavy duty scotch Brite in my experience (green and yellow sponge). I use it sparingly for really badly stuck on messes, and mainly stick to zero scratch scotch Brite (blue sponge). After cleaning and drying, I coat the cooking surface with grapeseed oil (any high smoke point, neutral tasting oil is fine) and then wipe it all out with a paper towel like I made a mistake. This makes a thin layer of oil that keeps the seasoning in good shape.

As for specific brands of carbon steel, unfortunately the brand I use (BICO) either doesn't exist anymore, or doesn't make carbon steel anymore (I got mine at a garage sale). I wouldn't recommend that brand specifically anyway since the metal is a bit thin. Generally speaking, what I like to look for in a carbon steel pan is a welded handle rather than rivets (easier to clean) and a thicker construction (thinner pans like mine can warp if they get really hot without food in them). If I had to buy a new one, I think I would try one of Darto's, Matfer Bourgeat's, or cast-a-way carbon's carbon steel pans. If you want a cheap one to try out before springing for a nicer one, restaurant supply stores sell lower quality carbon steel for really cheap (see Vollrath, Winco, etc).