So much good information!
I will take a different approach! Wont focus on brands, there are enough good suggestions already, I will focus on process....
All I can say is that there is no perfect all around pan, period. One thing Ive learned after cooking for decades is that with practice you understand how different materials react, conduct heat, stick, etc. Therefore you need to have different pans in the same way that you need a wrench and you also need pliers because they work for different purposes and situations.
Sure you could use stainless for non stick optimum situations but the results would not be optimum, So, start cooking and find the right pan for the dish, say... cast iron. Find dishes that work for that pan... make mistakes and then find the right pan for another dish, research, borrow, sell, do more research and before you know it you will have a very well crafted set of tools and you will know exactly how and when to use them!!
Understand variables, limitations of pans and how burning temperatures of oils work, then try cooking the same ingredient in different pans, now change the temperature in the same pan... fine tune until you can tell the material, characteristics of the tool given the task.
Good luck!