Of those plug-in types, writing a “Nyquist” plug-in is by far the easiest option.
IMPORTANT
Nyquist scripts and plug-ins are written in “plain text”. To write Nyquist code, you need to use a plain text editor (I recommend NotePad++ https://notepad-plus-plus.org/). Do NOT use Microsoft Word or any word processor, because these do not use plain text. Microsoft NotePad is NOT recommended as it will frequently cause strange problems due to it messing up character encoding.
We have quite a lot of information / documentation for Nyquist these days, though we are still a bit lacking in tutorials.
The “landing page” for Audacity’s Nyquist documentation is this page in the Audacity manual: Nyquist - Audacity Manual
There’s a list of reference documents here: Manuals and reference material (If you are interested in working with Nyquist, it’s worth bookmarking the links in that post).
At it’s simplest, Nyquist can be run in the “Nyquist Prompt” Nyquist Prompt - Audacity Manual
The simplest form of “Hello World” using the Nyquist Prompt is simply:
(print "Hello World")
The Nyquist Prompt is very handy for testing code and for running short snippets of code, but for more complex scripts, and for usability, there are advantages in creating a self-contained Nyquist plug-in that may be installed in Audacity.
A Nyquist plug-in is simply a plain text file, that begins with some “header” commands, followed by the Nyquist code. The “header” commands tell Audacity that the text file is a Nyquist plug-in, the name of the plug-in, the type of plug-in, and what controls (“widgets”) are required in the plug-in’s GUI (if any). If a GUI is defined in the header, then Audacity creates the plug-in GUI, and passes the values from the GUI to Nyquist. More details here: Missing features - Audacity Support
A simple “Hello World” Nyquist plug-in:
;nyquist plug-in
;version 4
;type tool
;name "Hello World"
;copyright "Released under terms of the GNU General Public License version 2"
(print "Hello World")
When installed, the above plug-in will appear in the “Tools” menu as “Hello World”.
A simple “Hello World” plug-in with a GUI:
;nyquist plug-in
;version 4
;type tool
;name "Hello World GUI"
;copyright "Released under terms of the GNU General Public License version 2"
;control text "Enter text" string "" "Hello World"
(print text)