I just updated to macOS High Sierra. What's the best way to use Time Machine under Apple's new APFS file system. Should I use Disk Utility to convert my external Time Machine volume to APFS?
Time Machine supports APFS as a source and not a destination. You can't backup to an APFS destination disk and Time Machine will inform you that the disk needs to be HFS+ if you attempt to do this.
Right now, there's nothing you need to or should do. Your internal disk has been converted to APFS and your backup disk is still on HFS+, so Time Machine will function as it always has, and will continue to inherit previous backups despite the difference in format. On a future date when Time Machine supports APFS destinations, you can convert your backup disk.
Until Time Machine is updated, it does not support APFS on the backup disks.
Apple needs to resolve the linkage to folders first. Hard links to directories are not supported in Time Machine, Apple will need to reprogram TM. I'm sure when they have Time Machine updated, they will make the change to APFS seamless.
In my opinion, you should avoid APFS on external hard drives, as you will have trouble restoring it if the disk has serious trouble. See my post here: https://discussions.apple.com/message/32385656#32385656
According to Apple's web site:
You don't need to change any Time Machine settings to back up APFS-formatted disks. Any Time Machine share points must be shared over SMB instead of AFP.
I wouldn't format your backup drive: it doesn't support APFS unless it is all flash. I would just try to do a Time Machine backup and let it worry about it. Since Time Machine backup are not image backups, I am assuming that the OS will handle the reading and writing of the backup records.