I think you might be looking at something else,
You really only need 1 or 2 of these.
and maybe a 12" version if you want to cook for more people.
https://www.amazon.com/Matfer-Bourgeat-062003-Frying-4-Inch/dp/B0040ZPPSS/
I would avoid nonstick, unless weight is a big concern (nonstick will be aluminum and lighter) or you want that plastic handle ergonomics. The reason to avoid it is you don't need it for eggs and they're wasteful (see advice above about throwing them out when coating starts to flake). Also ugly especially if you say burn the handle a bit or the coating flakes off. Can't say much about toxicity, since all those green ceramic new ones claim they're not toxic.
So what to get: carbon steel such as, Matfer Bourgeat 062003 Black Steel Round Frying Pan, 10 1/4-Inch, Gray https://www.amazon.com/dp/B0040ZPPSS/ref=cm_sw_r_apan_glt_fabc_9G8QMJEJKNM2BXWZNSPZ?_encoding=UTF8&psc=1
Season it first, (I used potato peels and a little high smoking point oil like avocado oil or grapeseed, canola etc)
Make sure to preheat well before you use for eggs - no 1 reason people mess up frying anything is they don't preheat enough. Check for example how Pepin makes eggs (in this video he does use nonstick but in others he doesn't) https://youtu.be/X1XoCQm5JSQ
I've used mostly cast iron pans and SS, but a cast iron is heavier than Carbon, takes longer to preheat, and longer to season well (untill it becomes smooth inside - you could help by sanding to fine grit if you want to speed up). As with carbon you do need to dry Carbon pans on stove with heat to avoid rust.
Upshot: carbon steel is lighter than cast iron, is easy to make non-stick, can be used in oven and for almost anything. I would use a SS for things involving more steam, liquid or acid like lemon juice. But you can still use carbon for those, just may need to reseason a bit before putting away. Also it's so non-stick that you generally don't need soap to clean it, just water and easy scrub, and I would avoid soap again because may need to reseason.
$32 should not be too lofty a price for someone wanting something to last the rest of their life and a 10" pan is kind of a do it all size unless you need a small omelette.
https://www.amazon.com/Matfer-Bourgeat-062003-Frying-4-Inch/dp/B0040ZPPSS
It depends on your heating elements.
Gas, you probably have the ability to heat up a 12" to the edge.
But electric coil will never heat a 12" anything properly.
Gas wraps around the base and up the sides of a pan/pot, while electric is a static element that sits and heats one part of the pan/pot while relying on the pan/pot materials to move the heat to the edge (resulting in uneven heating, unless the pan is smaller than the burner).
Pro kitchens usually have crazy-powerful gas stoves: a chef could have a favorite pan at work that they'd never even want to borrow and take home, because it'd be useless.
That said, economically-speaking, between this $30 10" Matfer-Bourget and this $55 12" Matfer-Bourget, I'd be more inclined to buy two of the 10" than one of the 12".
That's just basic math: a 10" pan is 30in^(2) while a 12" pan is 38in^(2) - two 10" pans gives you 60in^(2) of cooking area for the same price plus it lets you cook two different things if you don't need so much space for one dish.