You should not use the internet to do such a transfer. Apple has given us an app specifically designed to do these transfers. It is Migration Assistant. Easy to use, but it is important to carefully follow the directions. Definitely use a Usb cable between the two computers. The basic steps are the following.
Start both computers up and begin the setup process on the new Mac.
At some point you will be asked if you want to transfer data from your old computer. Say yes.
Connect both computers with a USB cable. Do not use Wi-Fi for the transfer. It is too slow and your data is likely to be corrupted due to the volume of data to be transferred.
Open the Migration Assistant app in both computers and follow instructions.
You will be presented with some options as to what to transfer. Click the appropriate boxes.
I suggest that you copy your preferences and settings.
You can either have Migration Assistant copy your files or copy them over manually. You can not selectively transfer files.
You can either have Migration Assistant copy your apps or you can elect to download and reinstall them. In either case, some of them may require that they be reregistered to work in the new computer. In some cases, apps may need to be upgraded to work. There may be a cost to upgrade some of them.
Your old operating system will not be transferred.
All files in the old computer will remain intact. They will not be erased.
The transfer may take up to an hour, more or less, depending on the volume of data to be transferred.
Enjoy your new Mac.