I get the sense that backing up a machine onto a Hyper-V / virtual drive is an appealing strategy ...
No sir, it's not. It's not possible to backup to a virtual machine.
Backing up to an external hard drive is simpler and faster. You can't do this with Windows, but it's easily done with backup software.
To make an exact copy of your entire hard drive that you can restore at any time, use an image backup program like Acronis True Image, Macrium Reflect (my own choice) or EaseUS ToDo Backup, among other great choices.
To backup only your personal files you could also use an image backup program, or you can use file-and-folder backup software like Backup Maker or Backup4All.
Either type of software can do incremental and/or differential backups, which can be a good strategy.
To do this with a virtual machine you would need to virtualize the physical computer with an application like MVMC (Microsoft Virtual Machine Converter) or Disk2VHD (from Iperius Backup) which has to be installed on a second computer. You cannot make incremental backups this way. Then, to restore the virtual machine, you'll need an additional V2P converter. This is excessively complicated and time-consuming.