As someone who learned way more about pans than I really want to know, let me say that a good cook can make good food in any pan, however some pans are more suited to tasks than others.

First off, searing meat in a non-stick pan (traditionally Teflon) is a bad idea, the pan can reach temperatures that produce toxic gases, and are known to kill birds that are more sensitive to them than we are. The coating that makes them nonstick isn't very durable and will at most last a few years before being useless. While other kinds of pans are likely to outlive you.

Other common pans include cast iron, stainless steel, carbon steel, and ceramic non-stick (non-toxic, but are delicate)

Specifically for searing meets, my favorite is stainless steel. It holds heat similar to cast iron, but is slightly more conductive and can transfer a lot of heat to sear meat. Meat also literally bonds to pan and can be used to make great flavorful sauces with deglazing. Cleanup is easy, if anything is really stuck just boil water in it to loosen. Alternatively stainless steel holds up decent in a dishwasher. Cleanup can't be easier than automatic. However, stainless steel is still quite heavy.

For general purpose cooking my personal favorite is carbon steel. It's seasoned like cast iron and can be quite nonstick, but is much lighter making it feel very similar to nonstick pans, which are made with aluminum.
I won't lie, seasoning has a learning curve. Seasoning is very tough under some circumstances, and very delicate under others. Notably acid will eat the seasoning away.

Cast iron is great, but it is so heavy that it is inconvenient to use.

All will work with induction, except for cheap aluminum nonstick pans

Give cast iron a try. It's cheap, lasts forever, and can be just as non stick as any "non stick" pan. Just clean it out and oil it again after use.. Or leave it be.. I'm not here to start a cast iron cleaning war

The cast-iron I've been using for the past 16 years was probably made in the 1940's in Ontario and will likely still be around after I die, unless someone leaves it in the rain or something. With coated pans I'd have to buy new ones every four years or so (which is not only costly but environmentally unfriendly)... not to mention the health risks of using non-stick, which are negligible IF you never forget it on a hot burner; it will overheat and the coating will break down and leach into your food.

Gas ranges also release toxins into the air which can only be properly extracted if you cook under a fume hood, like one you might find in a chemistry lab... even the best kitchen exhaust fans can't exchange the air that well and you're left breathing in carcinogens everyday when you cook your meals. So, if one uses a coated pan on a gas stove... well.

IMO the best choices are anything except coated pans on an induction stove. I read somewhere induction stoves are more efficient but I've never actually looked into it. Cast irons can certainly be a pain in the ass to maintain, but once you get a good coating on there it's smooth cooking until something acidic is cooked with it, or a roommate puts it in the dishwasher for you... which is why it's good to also have a steel pan also. I've never eve heard of copper pans lol, sounds expensive.

Cast iron pans are fucking heavy. As soon as I tried picking one up, I knew I don't want to cook with that on a regular basis.

I have gone through several non stick pans and they all suck because they will wear out relatively quickly. Eventually things will start to stick, and then you are in trouble because you have to treat them gently to avoid scraping off the nonstick coating, so you end up in a catch 22 situation where you can't actually scrub stuff off without making it worse.

I switched to a stainless steel pan about a year ago and I love it. The weight is somewhere in between cast iron and most nonstick pans. I've never had anything get horribly stuck to it, and it's not difficult to clean because you can use abrasive sponges or whatever without damaging it.

Ceramic non-stick is pretty great. I've used cast-iron and it's fine, but it's kind of fussy when it comes to cleanup.

I love my cast irons, I have a carbon steel one, that is even more work to care for, but gets really hot and is great for searing. I would like a stainless one for more of a nonstick option though.

Sadly, metal hot make food hot is not the only factor. It's also the speed and responsiveness of the pan. If you have the money, look into 3-ply pans, stainless bottom (for induction, but works with everything), aluminum interior (for eveness of heat throughout the pan) and stainless interior/cooking surface. I've had some of my pans for 40 years and they look brand new. They're just as easy to clean as non-stick, if you use wooden utensils for a quick scrape before cleaning. All-clad is probably the best brand, I bought some recently, and they are just as good as the old ones I have, very rare these days. They can be found on eBay and craigslist used, and the used are just as good (have a few of those as well).

I love my cast iron pans, especially for searing and tortillas, but for sauces and risottos, 3-ply is a great option. It's really about the responsiveness.

Last thing, ceramisised cast-iron (like Le Creuset) is terrific for deep frying.

A good quality stainless set is far superior imho, you can actually keep it clean and dont have to mess around with seasoning it. Also, if you drop it, it won't break your foot and/or flooring. Cast iron is a fad that frankly is already dying out.

Cast iron flavors the dish some. A seasoned one adds the oils and other stuff used to season it as well.

No

Stainless is just a piece of metal. Indestructible. No rules. Requires some skill to avoid food sticking, but it is doable. You can cook anything, anyhow and clean it however you want.

Non-stick is... well, non-stick, but there's a ton on rules. No metal, no dishwasher, no stacking, ... However they are really non-stick, no skill required.

Cast iron is like a middle ground. You cannot ruin the pan, but you can easily ruin the coating: no wine, no tomato, no lemon, no soap, no dishwasher, etc. And the non-stick effect is weaker than Teflon or ceramic, it still requires skill to use.

As a hobby cook I have never gotten into cast iron, I use 90% stainless steel and 10% non stick (mainly for pancakes) and for my wife who doesn't want to fiddle with temperatures with stainless.