Short answer: plug the drive in, open System Settings, General, Time Machine, and add it as a backup disk.
That is the fastest route and it works. The rest of this page is about what it costs you, and what to do if it is not the right answer.
macOS will offer to erase the drive. It is not being awkward: Time Machine needs its own filesystem and its own snapshots, so the disk becomes a Time Machine disk and stops being a general-purpose one. Anything already on it goes.
rsync ships with macOS and copies a folder to a drive without formatting anything:
rsync -aE --delete ~/Documents/ /Volumes/Backup/Documents/
-a preserves permissions, symlinks and timestamps. -E keeps macOS extended
attributes and resource forks, which ordinary rsync flags throw away. --delete
removes files from the backup once they are gone from the source, which is what makes it a mirror.
Read that last sentence twice, because it is the trap. A mirror has no history. A file you deleted last Tuesday, or a document a piece of ransomware encrypted this morning, is gone from the backup the next time the command runs.
Drop --delete and the backup keeps everything, but then it also keeps every file you
have ever deliberately thrown away, and it still holds exactly one version of each.
Whatever wrote the backup, nothing has read it back. A truncated write, a cable that dropped halfway, a disk quietly failing, a half-finished cloud upload: from the outside all four look exactly like a healthy backup, and you find out on the day you need it.
Checking by hand means recording what you wrote and comparing later:
find /Volumes/Backup/Documents -type f -exec shasum -a 256 {} + > ~/backup.sha256
and, a month later:
shasum -a 256 -c ~/backup.sha256
That is genuinely worth doing. It is also the thing people mean to set up and never do, which is why Copy Shelter does it on a schedule and tells you what it found.
Any drive your Mac can write to will work, including a USB stick. Two things matter more than the brand:
An external drive still lives in the same building as your Mac, which is why the 3-2-1 rule asks for a copy somewhere else as well.
For Time Machine, yes. It needs its own filesystem. For rsync, Copy Shelter or any other tool that writes to an ordinary folder, no: the drive keeps whatever is already on it.
With Time Machine, yes. Each Mac gets its own backup on the disk, and they do not interfere. Just remember that one drive failure now takes out both.
Time Machine runs hourly on its own. For anything you set up yourself, daily is a reasonable floor. The right question is how much work you are willing to redo, and the answer is usually less than a day's worth.
It needs to be connected when a backup runs, which for Time Machine means most of the time. A drive that lives in a drawer is only as good as your memory of plugging it in, so pick a tool that tells you by name when it has not seen the disk in a while.
Time Machine restores during setup through Migration Assistant, which is the smoothest recovery on any platform. No backup tool, Time Machine included, restores the sealed system volume itself: macOS always comes back from Apple.
Want the backup checked? Copy Shelter writes to any folder, encrypts before anything leaves your Mac, and reads the backup back on a schedule. Free for one location.
If the drive you have is a network one, backing up a Mac to a NAS covers that instead.