If your cooking appliance is gas, electric element, or radiant almost every type of cookware set will work. However you may pay more for a set that is designed for Induction so look at the specifications before making your purchase. Also radiant cooktops have a smooth ceramic surface that can be scratched. So pay attention to the bottom surface of the pans and don't slide pans across the cooktop. Induction cooktops have coils that generate an electromagnet field that cause the pan to heat. Therefore you must buy cookware that is magnetic. So take a magnet with you when shopping for induction ready or induction capable cookware, if the magnetic sticks to the bottom of the pan you picked the right cookware. Also as I mentioned above induction cookware is generally more expensive.
Another consideration is how many pans and pots do you need? Cookware sets come in various piece sets including 7, 10, 12 and 15 piece sets. Some include tools like spoons, spatulas that are part of the overall set count. So a 12 piece set may include tools you already have and don't need. But remember you must use plastic or wood cooking utensils with non stick coated cookware. Ceramic coating is more forgiving but will scratch if you use the wrong utensil.
Another thing to consider is will you place pots and pans in the oven? Some cookwares set are oven safe to 500 deg F some to 350 deg F and some cannot be put in the oven.
Also consider whether the cookware is coated with a non stick coating or a ceramic nonstick coating. The nonstick ceramic coating offers much better scratch resistance than just nonstick. Also lot of nonstick coated, both ceramic and non ceramic, cookware comes in colors and is dishwasher safe.
The most durable type of cookware is stainless steel. Top of the line is premium grade 18/10 stainless steel. Most stainless steel cookware sets are manufactured with a multi element base of steel and aluminum core some more higher price sets also include copper. This multi layer sandwich produces a more even heat eliminating hot spots. One more design upgrade is riveted handles offered buy some manufactures.
One more thing to consider between stainless steel and non stick coating cookware is stainless steel will stick more easily than non stick coated cookware. So if you switching from non stick to stainless steel be careful until you learn out to use your new cookware.
The thickness of the pots and pans is something else to consider. The thicker the material the longer the pan or pot will last. Thinner material could warp when exposed to high heat. Thickness also helps to produce a more even heat like you get with stainless steel pots and pans with a multi layer base.
Shopping for cookware sets can be confusing but I hope after reading this article you are more informed and can make a decision that provides you with the most cooking enjoyment and value for your money.