A Mac mini works great as a Remote Time Machine. You just need to:
- Enable File Sharing
- Give each user their own login for security.
- Plug in an external hard drive for plenty of space
After that, anabolics the user will just need to connect to the drive using afp://000.000.000.000 (ip address) and they can backup using Time Machine.
Do keep in mind that setup like this works, but does not have an encrypted transmission of data.