We have been cooking on induction for over a decade, wouldn't leave home without it. Beyond magnetism, one of the important properties for induction cookware is in the layers or plies of steel running from the center-bottom of the cookware to the outer edges and then up the sidewalls. This helps with transferring the heat evenly around and up the sidewalls of the cookware. Some of your lower cost cookware does not have the plies running throughout and up the sidewalls. It's this property which is not a hard and fast technical requirement that used to scare people away from induction, along with the no copper bottom and cheap aluminum stuff since those won't work. You want something of reasonable quality and will not change shape when heated. Some cheaper cookware will go from being flat-bottom to rounded when heated and that causes the outer edges of the cookware to rise off the glass and become less efficient to heat, not to mention rock back and forth on a glass top range.
At home we use All-Clad cookware, if you don't mind dropping the bux on it, it's the best you can buy. Just look for anything with the induction symbol on it and is multi-ply, or visit something like a Williams and Sonoma for guidance. Alternatively
Cuisinart makes a great knock off that we also own and I find myself reaching for it more often for every day abuse (also available at
Costco). Lastly, I've heard generally good things about
Costco's Kirkland brand of stainless cookware. You'll note that on pretty much all of the recommendations, they're all tri-ply which is the
key to success.