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.
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.
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 $$$.
That said I wish they'd test the Granitestone Pro as other reviewers have said the Granitestone holds up better than other ceramic pans.
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.
My primary use case is high heat wok cooking. A lot of ceramic woks exist, they just don't last long!
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.
Ceramic
Cast iron
Stainless steel
In that order, in my opinion.
I don't buy frying pans, so I take what I can get.