Can I use USB or Firewire to connect my current Mac mini to a new one to migrate data?

During the initial new Mac Setup, Migration will look for the other Mac on the Ethernet connection to Migrate from.

If you have already missed that boat and setup the new Mac, then you will need to establish the Ethernet connection using the Network Preferences/Settings

If you have already setup the new Mac mini, then your options are:

1. erase the new Mac mini and start over.
2. establish an Ethernet connection and then use Migration Assistance in the new Mac mini’s Utility folder.

The most reliable and quick way to migrate is to use a backup drive. see this Apple Knowledgeable article: Back up your Mac with Time Machine - Apple Support

Everyone needs a backup - computers fail and today with our computers hold contact information, photos and videos, music, etc, a drive failure is catastrophic. The fact that we can use this TimeMachine backup to move to a new computer is an added plus. It is fast and reliable.

lease rewrite your question(s) for better clarity. What specifically are you wanting to 'migrate'? If you wish to use your existing keyboard and mouse, then just connect them to the new computer using a USB cable and port on the computer. When you set up the new computer, you select the Wi-Fi network in System Settings. If Comcast is your email provider, then use the Mail app to set up an account in the new computer. Better yet, you clearly need assistance, so I suggest you get some help.

First, I assume that you are using Migration Assistant to do the transfer. Second, I would only use a wired cable to connect the two computers Wi-Fi and networks are just too slow for the transfer of this much data and almost always fails.

+1

Do not use WiFi has this connection can drop. Just use a TM backup (from old Mac) drive connected directly to your new Mac via USB and no issues.

What I was trying to say is to only use a wired connection between the two computers to do the migration. Wi-Fi should not be involved.