What material is the best pan you own made of?

I love Le Creuset enamel pans and pots!

I use my All-Clad large pot with two handles all the time; I mean, all the time. The small All-Clad saucepan gets a lot of use, too. They clean easily, conduct well, are easy to handle, all-around fine workhorses.
For less frequent use but a real favorite, is my oval Le Creuset gratin dish. It's a beauty, and for gratins you simply can't find anything nicer. I know nothing about styling, but I do know that the ones like mine that I've seen in beauty shots look so classy.
I have a large flat generic lid with a heatproof handle that fits on my large (12") skillet, and on any other pan with two handles (i.e., nothing angled up to get in the way, at least for the smaller ones). I got it a restaurant supply store. I put it in the indispensable, real keeper category. It's of excellent quality, but not a fancy brand.

I love the heavy, stainless steel lined copper skillet I was given years ago. Mr T bought it at Sur La Table (their brand, made in France). Another real favorite that I reach for constantly, it conducts perfectly, while turning heads with its classic beauty. Plus, it goes into the oven - so helpful.

I hope this helps. ;o)

Btw, what is your stovetop? I think pots and pans design and material depends a lot on it.
I love 3-ply stainless steel with copper on the middle. Very easy to use, rust-proof, good at conducting heat and no heat spot. Because we have ceramic stovetop, I cook even all my stir fries &fried rice in pasta pot because it has largest (flat) contact with heat source and I never have problem turning them with spatula.

Cast iron. Lodge skillets, le Creuset Dutch ovens.

I wouldn't want to say anything about "best"- depends too much on what you want from it, and you have to decide if price, storability etc. are part of the equation, but the pan I reach for most (cooking for 2 people) is probably my cheapo Joyce Chen 91/2" wok, with a lid (Ace Cook) I bought separately. The pair was probably no more that $25 on Amazon, but it usually seems to be the best tool for the job. After experimenting with some expensive nonsticks, I think I'm going back to buying $20 Teflon pans and replacing them regularly- the expensive ones don't really seem to last much better.

Stainless steel rondeau.

Valentina, so glad about the new kitchen, congrats, you must be so excited!!! I might be a little bit weird in this respect, but I use my Le Creuset Dutch ovens for almost everything. My favorite is a wide and shallow round Dutch oven, it is about 4 inches deep and 12 inches in diameter and is wonderful for browning vegetables, sautéing and caramelizing onions, reducing excess liquids and slow cooking. I do not make too many stir fries, but when I do, I use it instead of a wok because of the large surface area. However, I bought it about 15 years ago, and not sure if Le Creuset carries it any more... And I know this might matter to you, Dutch ovens are also great for styling, especially some of the muted colors (gray, aubergine, truffle, slate, cream), both Le Creuset and Staub have a range of exciting new colors.

I swear by my carbon steel pans, and deglaze with wine all the time. Only thing - you can't wash them. You need to clean them out with kosher salt.
My favorite pan is one you can only find on eBay... It's an original Cuisinart 5.5 quart deep saute with lid that has a copper pocket on the bottom. The original cookware was made in France. What's on offer these days is from either China or SriLanka - not sure which.

Since you already have a copper and cast iron, I would strongly recommend getting a wok with a lid (yes I know that sounds daunting). These are high-capacity, and can handle anything from stir-frying, braising, steaming, frying, deep-frying, and even smoking. If you do, make sure you get one that's light enough for you to manage with your left hand (if you're right-handed), that has a lid, and is not cast iron (which makes acids a no-no and also makes it much heavier). One last thing, if you have been blessed with a gas range, then go for a wok with a rounded bottom, otherwise stick with one that has a flat bottom.

If I had to pick one pan for dessert island (or all) cooking, it would be a deep covered cast iron skillet (or Dutch oven)....for versatility (soup to cake), compatible with every heat source, low cost, sturdiness.
2nd choice is a pan with a conductor metal protected by or sandwiched by a surface more convenient for cooking (e.g. enameled cast iron, steel sandwich with copper in between).
BTW, the no-acid thing for cast iron is more about not doing long cooking or storage with an acidic sauce or liquid, because of the interaction with the pan. You could deglaze with stock and add a bit of wine off the fire for flavor, or even a very quick deglaze with wine.
Avoid aluminium. While data linking it to Alzheimers etc. are inconclusive, they are worrying.