am I right that as long as I know what materials they are made up of and the dimensions is okay for me, then it doesn't matter what brand it is right?
I am only interested in stainless steel pan because I believe that easy-to-clean pan could be very dangerous to health over time especially if it's scratched.
What are the different types of stainless steel and which one is the best and safetest? I remember there are different numbers or grades, I don't remember clearly
Those numbers you are probably thinking of are listed as 18/10 and 18/8 - percentages of chromium and nickel, the higher the numbers, the harder and more stainless. I don't see the grades like 305 and 316 on food stainless - I see these for screws for my workshop, and, again, the higher the more stainless. 400 grades are magnetic, which is what the outer layer is of induction ready pots is, but they just say induction ready.
Many cheaper pans out there have a sandwich disk just on the bottom, not up the sides, as the better ones. The heat goes up the thin sides, and burns the food frequently.
ATK did some severe tests on these pans, one of which was to heat it up over high heat, then plunge it into ice water - not something any of us will be doing at home! But this severe temperature change can cause warping of the metal. And some cheap pans are manufactured with a "hump", which is supposed to flatten out when heated, though this doesn't really seem to work.
A good, affordable brand I found, when I replaced a number of my pans with induction capable pans, is
Cuisinart. I also got some good pans from Williams Sonoma - induction capable skillets, with NS ceramic coating. Not sure how this stuff does in the long run - too soon to tell. But it's the better option to PTFEs, which I assume is what you are concerned about, with "easy to clean pans".