Just about any USB external HDD (or SSD) will work.
One thing to be aware of:
Some pre-built drives (Seagate and WD, at least some of them) come with software installed "at the factory" by the manufacturer.
This software is designed to "be helpful" but often ends up "getting in the way" of things with the Mac OS.
I recommend that you REMOVE any pre-installed software, and then erase the drive to "Mac OS extended with journaling enabled" (using Apple's "Disk Utility").
Do this before assigning the drive to backup duty.
For backup, and my opinion only, I recommend a "cloning app" instead of Time Machine.
The two apps that have this market cornered are
- CarbonCopyCloner
and
- SuperDuper.
I like CCC because it can clone over the recovery partition as well.
Both CCC and SD can work with HFS+ and APFS drives.
