I don't like non-stick anymore because the coating eventually gets all scratched up and doesn't work as good. Idk how it gets scratched up, I never used metal. My ex did, so maybe it was her.
Cast Iron, if maintained well (i.e just don't cook anything too acidic. You don't usually need to re-season), lasts forever. It's also great for when you want to sear something without the pan cooling down once you put your food on it. Because it's thick and stores a bunch of heat. Yet somehow it also gets hot pretty fast.
I don't get stainless steel personally. Apparently to get things to not stick, I should be using MORE heat? But I already use a lot of heat! On the up side, they get hot really fast.
Copper and carbon steel I've never used. I hear carbon steel is similar to cast iron in many ways, but easier to maintain?
If you're doing a new build, definitely go induction. Electric sucks because it's kinda slow-ish to get started, gas sucks because either you need to have a gas line built to your house if you don't already have one, or you change out the gas container every now and then (and that thing is heavy, mine's 17 KG of gas + whatever the huge chunk of metal weighs, which is definitely more than 17 KG). Plus the whole issue of, y'know, freshly burnt hydrocarbons (yay CO2 and potentially other gases). Oh and gas explosions aren't common, but they can happen!
Only downside of induction is that if you lose power, you can't cook. A wood-burning stove as a backup is excellent in this case, because depending on what your heating system is, you may also lose heating if power is gone.
It's not particularly good to use indoors and very impractical to use for multiple meals when it's like -30 outside. Also I'mma gatekeep now and say that BBQ should be wood or charcoal, not propane. More smoky flavor.
That said, obviously one should own a BBQ of SOME sort if they own a house. I think it's legally mandated in my country that any home with even a tiny bit of land around it, needs to have something that can be used to produce burnt shashlik and sausages.