As noted in the welcome tutorial Lua is plain text, so you can edit it in notepad, but you'll probably find you want something a bit better.
The editor you use is a personal preference - so it's up to you to choose one for yourself. The editors below are listed because they are the most popular editors in the Garry's Mod community.
Sublime is a very good text editor as it is appealing and effective, it's also highly customizable and easy to use. It offers a number of features that will aid you in development, such as syntax highlighting, a minimap and a number of hotkeys. It also has a great package manager for installing plugins. The following are a few recommended packages to install:
Visual Studio Code is a lightweight counterpart to Visual Studio, similar to Sublime. It's customizable with extensions and is fairly easy to use. It has built in git support, and a large set of extensions in the marketplace. Here are some extensions that you should install:
If you use Visual Studio then it might be more comfortable and convenient using it to edit Lua too (rather than learning a new editor). The free versions of Visual Studio are called 'Express'. There's a good page about Lua plugins on the World Of Warcraft Wiki.