What file service should you use with network drives and Time Machine?

What kind of networked volumes formatted with which methods can you use with Time Machine? A reader queried me on Twitter, trying to understand from their past experience and Apple’s current documentation, and I agree that it’s not very clear, because of Apple’s inclusive but non-specific language.
Apple used to favor the Apple Filing Protocol (AFP) file service for network drive sharing, local and remote. However, it’s deprecated AFP in favor of the Windows-compatible S