Sorry for the non-answer, but two things:
First, I'll second namhod's recommendation for cast iron. My main cast iron skillet was left for scrap. I had to wire-wheel off a crapload of rust, but the result was a glass smooth pan that's given me close to thirty years of service once I had a good season on it. The only time it leaves the stove top is when its buddies, my twin Lodge griddles, need the room.
As for stainless, the trick with eggs is to use two different greases in the pan. Butter / oil is the most common, but even two different oils work. My wife is lactose intolerant, so I'll use a 50/50 olive oil / coconut oil mix for her. As long as you have a good temperature on it, eggs won't stick.
But trust namhod on the cast iron.