Modern stainless steel pans with clad bottoms can be as good as copper pans. McGee developed a simple technique to test the heat distribution where he fits a piece of paper to the bottom of the pan, placing the pan over a burner and carefully watching how the paper browns. Thick aluminum, clad bottom stainless, and copper all worked equally well.
There are differences that relate to the techniques used in cooking. A thin copper pan is great for melting butter or chocolate straight on the burner. Modern air-gap wall stainless steel pans hold the heat better and work better for simmering or boiling. Copper is harder to upkeep.
Pans will develop hot spots, even copper which is the better conductor. Until we get graphite added to the cladding or some other exotic material to distribute the heat, thickness will matter the most for even heat distribution.
I have read several consumer tests and reviews of pans and they fail to note that thermal conductivity and thickness can both be used in practice to balance the temperature distribution and heat flux in a pan.
This is quite common and pretty harmless. The scratches you see don't go very deep, nor are they very wide. My All-Clad saute pan is nearing 10 years old and has a ton of micro-scratches on the interior. It still performs beautifully.
That said, the scratches can grab onto proteins and cause sticking. However, this is simple to prevent with both oil and proper pan preheating.
When a pan is preheated properly the metal expands, essentially closing all of the micro-scratches. This prevents the proteins from grabbing onto them and getting stuck. You obviously need oil/fat to assist with this as well.
To properly heat a pan to the appropriate temperature I suggest using the water drop method. If you put a cold pan on heat and drip a drop of water onto it, the water will sit there for several seconds then boil away. As the pan gets warmer this will happen more quickly, fizzling away in a second or so. Once the scratches start to close something weird happens.
First, the drop of water will break into a few mini drops which scoot around the pan as they evaporate. This is a sign that you are almost there. When the drop of water stays whole (mostly) and scoots around the pan like a mercury ball, this is the perfect temperature. I the water instantly vaporizes on contact, you've gone way too far and need to let the pan cool down. At this point you should add your oil/fat, swirl it around, and immediately add your food. (Make sure the mercury ball of water is gone before adding oil).
Also note that the mercury-ball phase is definitely too hot for unclarified butter, and may be too hot for some extra-virgin olive oils. They may instantly smoke upon adding.
Again, it's important to have your oil and ingredients in place (mise en place) before you start. It's quite easy to skyrocket past the mercury-ball phase if you have to open your oil, pour, and then season your ingredients.
Best Answer
I've never heard of doing anything other than giving it a good cleaning, as you would with any new item before first use.
I've only heard of seasoning used for cast iron and carbon steel, not for stainless steel. Looking online, I did find instructions for seasoning stainless steel, but I'd be inclined to look at the paperwork that came with the pan -- if the manufacturer recommends doing something, follow their instructions. If they don't, just give it a good wash.