It may be difficult to get to happen in your relationship, because at least for me, my partner is insistent on using non-stick pans. If you have to have non-stick, ceramic or hard anodized are much healthier than teflon, although they aren't as non-stick so require some adjustments to cooking style.
The best things to use are cast-iron and cladded stainless steel. With both, you heat the pan more slowly to reach your appropriate temperature (you're looking for leidenfrost) and then you add oil, and cook. If you use healthy oils and heat before adding the oil, cast-iron is effectively non-stick once a seasoning develops and cladded stainless steel won't stick except with specific foods (eggs). But this is definitely a different methodology for cooking than most people are familiar with.
The other benefit of using non-teflon pans is you can use all types of utensils.
Just want to share what I learned from personal experience:
Don't give up on winning over your partner's mind. It may take a little while, and you have to be patient, diplomatic, and gentle. People are resistant to change. But it is not hopeless, and it is worth it in the end, because their health is at stake.
I used to have teflon cookware. It's great in theory. But in practice, I find indestructible stuff that you don't have to baby works much better for me. Of course, if you don't have much upper body strength, other approaches may work better.
Traditional cooking techniques [1] make use of the browned bits anyway, you don't get this as much with non stick cookware. I don't find stainless steel pans too hard to clean.
Stainless steel for most things (can't make eggs/pancakes though, they'll stick). Preheat the pan before using. After cooking, warm up some water in it and scrap away the stuck bits with a wooden spoon (or make a pan sauce).
Cast Iron or High-Carbon steel for steaks, eggs/pancakes, stir-fries (wok). You will have to maintain a non-stick seasoning and that has a learning curve, most people don't get it right at first. Make sure to always dry them as they can rust.
You can look at enamel or copper if you have the $$$.
I use two ceramic pans which are still as good as when I got them 10-15 years ago from a brand called ecosafe. Not all from the set made it, one got ruined by overheating.
Stainless is durable, but I suspect there are issues with chemical reactions between the food and bare metal.
I think that enamel is the best, being inert and durable, and old technology, though you also don,t want to drop or overheat it.
Cast iron is also good, just unwieldy and difficult to clean if you,re cooking meat, eggs, cheese, basically animal proteins.
Ceramic are OK, but nowhere near the non-stickiness of teflon. Some pans are the first couple of times you use them but lose it real quick.
Carbon steal is my daily pan now (lighter than iron skillet - it's what chefs usually use). Once you get a good coating of fat built up it's pretty decent non-stickiness, but you have to take a lot more care of it.
I wish teflon was more healthy because it's damn good for cooking with, especially scrambled eggs.
We've switched to carbon steel from cast iron; while it's easy to warp the carbon steel (and we have), it still works fairly well on our electric range. The seasoning is just as good as cast iron. A heavier high carbon steel pan might avoid the warping issue, but ours are all pretty thin.
