The main types of pans are:
There are many other less-commonly used types, like enameled cast iron, aluminum, copper, etc. And there are hybrids, like the Strata carbon steel clad pan.
If you could only have three knives in your kitchen, they would be — a chef's knife, a paring knife (or utility/petty knife), and a bread knife.
Here are the different cuts you should know: [1] [2] [3] [4]