Answer: Use Mac OS Extended.
Mac OS Extended, also known as HFS Plus or HFS+, is the file system that was used on all Macs from 1998 until the last couple of years. APFS is the new file system for OSX and it works well for an SSD drive. But you can’t backup to an APFS drive using Time Machine (even if the external drive is an SSD drive). It sounds a bit backwards I know but that’s the way Apple are doing it at the moment.
There’s a work-around: you can use a sparse image to create a DMG to back up to an APFS SSD drive, (see here). I would not recommend this because the Apple recovery mode will not be able to find your backup.
From Apple Support:
Important: You can back up from an HFS+ or APFS-formatted disk to an HFS+ disk; however, Time Machine can’t back up to an APFS-formatted disk. If you select a back up disk formatted as APFS, Time Machine offers to reformat it as HFS+.
[retrieved Oct 7 2020 from ‘https://support.apple.com/en-au/guide/mac-help/mh15139/mac’]
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How to move a Time Machine backup to a different hard drive.
This is not accurate. APFS is supported for ALL disk types for Time Machine as of 2020.
Time machine would not complete backups to my external drive formatted with APFS in Disk Utility, even though this is supposedly the preferred format. I phoned Apple. They told me to select the drive from within Time Machine instead of using Disk Utility and, if not successful, use HFS+ format. Just purchased a new drive. It arrived formatted in FAT. I erased in Disk Utility in HFS+ format, then selected the drive from within Time Machine preferences. The icon turned from orange to blue after short processing and Get Info shows the format is now APFS. Also did this on a 3 year old drive. The old one functioned fine and the new one is currently backing up, but presumed OK. Thank you for your information. It would be great if Apple would update their info and give thorough instructions!