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 fast, snappy, appealing, and effective text editor which is 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.
It's probably the best choice if you are a beginner at coding, but if you have a bit more experience, you may want to try Visual Studio Code instead.
Visual Studio Code is a lightweight counterpart to Visual Studio, similar to Sublime. Where it falls behind in snappiness in comparison to other text editors, it makes up for this with its extremely powerful IDE features, massive extension marketplace and wide range of one-click-install themes. It has built in support for Git, FTP & SSH and brings over many of the IntelliSense features from Visual Studio such as autocompletion, documentation-as-you-type, and jumping around your code via definitions and references.
- GLua Enhanced - IntelliSense, autocompletion, wiki documentation, syntax highlighting, color palettes, etc.
- GLuaLint - Automatic error detection + hints
- GLua Syntax Highlighting - Acidic - Just syntax highlighting + snippets
- GLua Syntax Highlighting - aStonedPenguin - Just syntax highlighting + snippets
Vim and Neovim are highly extensible terminal based text editors, Vim based text editors use a scripting language called Vim Script which is used for editing every little aspect of the program from the syntax highlighting to keybindings.
Vim by itself kind of sucks, you're designed to go in and play with Vim script, adding your own keybinds and customizing it to your liking.
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.