How to pick the least wrong colors

In the course of trying to solve a seemingly simple problem, I got a crash course in the fundamentals of color. The problem boiled down to picking nice-looking colors that cover a broad set of use cases for categorical data. The criteria for success are threefold: The colors should look nice. They need to be similar to Stripe’s brand colors. They should meet accessibility goals. In short, I need lots of colors in case I have lots of categories. There are many ways to pick good colors for data visualizations.