Tri-clad stainless are the best all arounders. You can get these as Vollrath Tribute, All-Clad, Trimontia(?) (costco), Calphalon, and a few other brands.

Used: Some tri-clad is induction compatible (stick a magnet to it) and some isn't. People tend to give away non-induction tri-clad to goodwill these days, so it's easy to find. The induction-compatible tri-clad is harder to find.

New: Some sizes and shapes are impossible to find at thrift stores so you can just buy it. The most cost-effective and high quality is Vollrath Tribute. All-Clad are almost as good but the little weenie handles are uncomfortable.

Avoid teflon, it always gets damaged. Sometimes you can find a teflon All-Clad pan and call the manufacturer to complain about the nonstick getting wrecked you can get them to swap it for a non-teflon one.