An app I made from my script with py2app doesn't work on newer versions of OS X. I was told that this was because the build was partially standalone, meaning it requires my version of wxPython, but doesn't include it. How can I make it fully standalone (where my version of wxPython is included), or not standalone, where it uses whatever version of wxPython the host has installed? Which would be preferable, and how can I check that it has worked if I only have one mac with one version of wxPython?
Make sure you are using the latest py2app, it looks like they've resolved some issues lately related to semi-standalone, perhaps that may affect your build too.
Use the Python from Python.org, not Apple's python installed with the OS.
Don't use the --semi-standalone flag or options like it in the setup script.

That should be all there is to it.  Last I checked creating standalone applications was the default when using the Python.org Python, and it by default should be copying in the other packages (including wx) that your application imports as well.  You can look inside the generated application bundle to see exactly what it is and isn't including and you can then adjust your setup script as needed.
Toggling py2app standalone?