Welcome to the forum, @Arne!
For a single file shared at the time of publication, without plans to maintain (and possibly improve) it over years, an update site is not necessary (in my opinion). I second the advice by @Bio7 to put it on GitHub and/or directly include it as a supplement to your paper.
Of course, if your code is very general and useful for others, and you expect improvements/feedback from the community as well, it’s certainly a good idea to 1) have the source code on GitHub (for other contributors) and 2) ship it via an update site (for users).
That doesn’t generalize. It all depends on the implementation. The ImageJ macro language is super fast for many applications, but it also depends on which plugins/commands you are calling in the macro.
To gain performance by direct calls into the Java API, or to achieve parallelization of demanding computations, a full-fledged scripting language (such as e.g. Groovy) is fully sufficient as well, and saves you the effort of writing an elaborate plugin.
Migrating from macro to a full-fledged scripting language is certainly doable, and in most cases straight-forward, but there can be obstacles depending on your task. For publication of a method description, I suggest to not invest too much effort in the first place. If it turns out to be useful, others might want to contribute, or you might want to improve performance, then you can still go that route.
In any case, I suggest making the code public and then ask here on the forum for advice how to improve/translate it.