Hi Mary Jay,
Thanks for coming to Apple Support Communities for help today.
We'd suggest using whichever method has been working for you the best. It sounds like that was with the Thunderbolt cable.
Since the issue seems to have originated on the old Mac, make sure you have followed: Move your content to a new Mac.
"Get ready
- Install all available software updates on both computers. If your old Mac isn't using OS X Lion or later, and your new Mac isn't using OS X Mavericks or later, follow the Mountain Lion migration steps instead.
- If both computers are using macOS Sierra or later, place them near each other with Wi-Fi turned on. If either one is using OS X El Capitan or earlier, make sure that both are on the same network.
- On your old Mac, choose Apple menu > System Preferences, then click Sharing. Make sure that a name appears in the Computer Name field.
- If you installed antivirus or firewall software on either Mac, turn that software off until after migration is complete."
On your new Mac, you can always follow Erase all content and settings on Mac and then start Migration Assistant completely over if you need to.
Have a fantastic day!