So I can use PyInstaller to make a one-file executable and to make a standard executable among other files in a folder.
But how do I turn Python files into an MSI installer so that it's fool-proof where it makes a shortcut on the desktop? (For distribution so that it isn't required for the user to have Python installed)
(When I say Python files to an MSI installer I mean the regular PyInstaller to folder output but with a way of getting a shortcut to the executable onto the desktop very easily for a regular user) (It doesn't have to be PyInstaller if there's an alternative).
Pyinstaller does not intergrate such a tool.
You could get a third party installer (some suggested here How to create a robust, minimal installer for Windows?) and add your output exe to it and install that way, if you choose the right tool you will be able to add to desktop (plus a lot of other actions such as adding to path ect).
Or you could use cx_Freeze which has it built in. When running the setup script just add the bdist_msi flag.
It can add to shortcut desktop but is fairly limited in other ways (or you may need to perform some hack).
To add to desktop with cx_Freeze see Use cx-freeze to create an msi that adds a shortcut to the desktop.