Use the Mac OS Disk Utility to format your external drive as MS-DOS (FAT), the PC should be able to recognize it. Copy the files (there may be a 2 GB size limit for any single file), and then plug the drive into the Mac. Don’t forget to format the drive back to Mac OS after you copy the files to your Mac… and don’t forget that formatting erases all data on a drive.
Or, you can get all the Ethernet configuration instructions you need using the Help menu on your Mac.
Or, if you have access to an external Blu-ray burner you could burn 25-50GB data files per disc.
HTH
This is me – this is what I do – https://web.mac.com/garymmw