Can't get past login screen
The system may have been joined to an Active Directory (or other kind) of network authentication domain that would make changing the local admin password not work for long.

On general principles I would save nothing on a computer that I bought from somewhere else. 

That said I would suggest:


Boot into Recovery Mode
Select Disk Utility
Reformat the hard drive (then quit Disk Utility)
Click on Reinstall MacOS


You will likely be asked to authenticate to your WiFi network and presented with the install screen of the macOS version that originally shipped with the Mac.

That should give you a clean slate from which to do as you please, including upgrading to a later version of macOS.