VS Code is an open-source code editor. You can find information on how to set up TypeScript here. VS Code is a popular editor for TypeScript because Microsoft teams maintain both VS Code and TypeScript, so it works well with the language; VS Code supports TS without any extra configuration. In fact, VS Code was written using TypeScript!
A common issue with VS Code and TS is when your editor and project versions are different, which can cause VS Code to display a possibly confusing error message. Instructions on how to handle this error are here
Atom is an open-source code editor maintained by a team at Github. Atom uses packages to add features, and there is an atom-typescript package available. To install it, you install Atom from the link above, and when you open Atom you will be prompted on the introduction page to look at popular packages. You can search for atom-typescript there.
Sublime Text is a popular code editor with support for most languages through installable plugins. It is free to try, but you will be regularly prompted to buy a license, which currently costs $70 USD.
Help us explain this better! File a GitHub issue at https://github.com/exercism/typescript/issues if you have suggestions, or submit a patch with improvements to the https://github.com/exercism/typescript/blob/master/docs/RESOURCES.md file.