The easiest way to clone is to have a hardware device just clone the drive.
If you can’t get the drive out, you could boot to recovery and use disk utility or asr to clone
the entire drive. That would save you from needing to ship the
computer back to where you can work on it directly.
Once you have it or the clone, I think you want export instead of backup. The latter exists to serve the restore process. When you say anyone can read, that implies you need an export that covers android, Linux, windows, Mac, across 10 to 20 years of operating systems.
You won’t go wrong If you set up time machine and let it format the drive on the assumption that to read it you take that drive to any Mac that’s newer to do the read and export if needed to narrow to a non-apple OS. I would not use two macs for this – much simpler to let the Mac with the data manage the backup. Target disk mode and ignore permissions might help, but you’ll back up a ton of data you don’t likely need if you only want documents.
Also, using migration assistant to move the account over also might help you simplify things if you get them both in the same room.