apparently all the in-house experts are on sabbatical, so here's my amateur opinion / experience:
the stuff we have is thin stainless steel with a copper flashed bottom. some it it is from parents/in-laws and is likely 60+ years old.
works great for boiling eggs / potatoes / etc.
not so great for making a cheese sauce - poor conduction, hot spots, all the stuff of legend.....
don't have any, but Tramontina has a good reputation in the price vs quality scene for stainless.
do not go with any of the high cost non-stick and/or anodized (aluminum) stuff -
non-stick only last a few months; anodized 2-3 years.
well, if used.
I exclude user reviews: "I love this stuff and I use it at least once a month . . . "
18/10 stainless is the bench mark. "ply" stuff can be a lot of marketing hype. a thicker bottom - in stainless usually aluminum 'encased' in stainless - works for more even heat.
"waterless cookware" - total BS - don't even think about it.
handles are an issue if you like to finish stuff in the oven. plastic "anything" will not hold up over the longer term.
yup. copper is reactive and copper will / does 'tarnish' / discolor rapidly.
how fast is rapid? one use on a gas stove. LP gas worse than natural gas . . .
if you want it to look pretty on a pot rack, buy el'cheapo stuff that is lacquered, hang it up and _never_ use it to cook with - it's only good for display.
if you're thinking copper bottom ala Revereware - copper is 2nd best at heat transfer, but at the thickness involved on Revereware - "true but meaningless" in reality.
if you're thinking solid copper pots ala Bourgeat and similar - it's the best - it's absolute superb at its tasks - but keeping it polished and pretty is a full time job. I have several pcs - I use it to cook with and really don't give a hoot that it's no longer shiny.
the primary thing about copper benefits is the rapid response to temperature input change.
copper does not work on induction tops.
electric coils respond many times slower than copper - no reason to use copper on electric coils.
gas cooktops is where the benefits of solid copper show up; the heat output of a gas flame responds very rapidly when it is made bigger or smaller.