My plugin needs to store a bunch of files generated by the users actions. Where would be the ‘correct’ place to put them? Should I put them in my package directory (~/.config/sublime-text-3/Packages/User/packageName on linux)? If so how can I get that location?

Yes, store them in the User package. If you are going to create many of them, use a subdirectory in the user package.
Alternatively you could also try sublime.cache_path() for temporary files, but I have not yet exermined whether this has any side effects (i.e. automatically cleared on update or similar).

Your actual package should not be a part of the User package however.

os.path.join(sublime.packages_path(), "User", ...)