"They suggest Time Machine (of course they would).
Now, to borrow an external hard disk and do that over the weekend."
Again, I'd suggest SuperDuper instead of time machine.
It's free.
You can download it by clicking this link:
SuperDuper is incredibly easy to use.
All you have to do (as a new user) is select the source drive (on the left) and the target (on the right, this becomes your backup).
When it's done, take it to the new Mac.
Hmmmm...
Have you already created an account on the NEW Mac?
Or... has it failed during the initial setup routine?
IF you've already created an account,
this could lead to problems in the future.
You should consider using the "erase all content and settings" option in System Settings to take the Mac back to "moment zero" -- like it was the very first time you booted it out-of-the box.
Then it will be ready for a completely fresh start.
Just follow the instructions (erase all content...) and the Mac should do the rest.
When done...
Connect the backup drive and start clicking through again.
When setup assistant asks if you wish to migrate from another drive, YES you do.
"Point the way" to the SuperDuper backup and give setup assistant time to "digest" things -- shouldn't take long.
If you want to migrate everything (I see no problem with that), just click "continue" (or whatever that button is).
Then give setup assistant time to do the migration.
When done, you should see your old login screen, just as before.
Good luck.