Is there a comprehensive backup and restore method that would restore my phone to it's exact condition: apps, widgets, configuration settings, messages, media, etc.?
If so, what is the best most efficient way to do this?
While you can auto restore contacts and apps, you might not want to automatically restore everything, especially if you are coming from an FDR because you had issues to cause you to do so. Restoring contacts is fine, but definitely I would not restore app data. Some 3rd party launchers like Nova, Go, and Apex etc... will allow you to back up your current set up and theme, but I know of no way to do the same with TouchWiz. You can use SMS Backup and Restore app in the Play Store to back up messages. Samsung Kies might provide some backup methods as well.
I have used JS Backup before and it works very well. It will back up SMS messages, contacts and everything on your phone including apps and settings. It will restore to your phone exactly as it is set up right now.
If you are running Lollipop on your S4 currently or plan to soon:
※The compatibility with Android 5.0(Lollipop) is at the moment unstable. We are currently investigating possible causes and we thank you for your patience.