can you use an ethernet cable or HDMI cable for migration assistant

rkaufmann87 beat me to it. When Apple dropped FireWire for Thunderbolt there was a period of time when we weren’t able to use Target Disk Mode and at the time I was working for an Apple reseller. My boss tasked me with determining the best solution. WiFi is too slow and times out. Ethernet should be a great solution and can be. But in my first go rounds I experienced more stalled migrations than I did successful ones. So at the time I concluded migration from a TimeMachine backup was the best solution - especially since everyone needs at least one backup and TimeMachine is a pretty decent solution.

Since then every summer I check out the current options and I still think a TimeMachine backup from an external drive is the optimal solution for most people.

Using Ethernet is not recommended due to a high failure rate.

When you buy a new Mac the easiest, quickest and most reliable method is to simply connect the old Mac's Time Machine External Hard Disk to the new Mac using a USB cable before you turn on the new Mac. When you start the new Mac for the first time it will startup Setup Assistant (SA), SA will get to a point where it asks if you are migrating from another computer, select Yes  and follow the on-screen prompts and it's done! It is THAT simple.

If you have already done SA on the new computer then simply connect the Time Machine External Hard Disk using a USB cable and launch Migration Assistant (MA) which is located in Applications - Utilities - MA. Then follow the on-screen prompts. 

The ONLY difference between MA and SA is MA will create a new user account that you need to log into.

Both SA and MA migrate applications (not 32 bit apps) , data files, settings, it does not migrate Mac OS itself. Some professional apps such as Adobe and Microsoft apps may require re-installing their apps as they will not allow them to be migrated. As long as you kept the security keys for installing their apps, it is not a big deal. 

Ethernet yes, HDMI no. https://support.apple.com/en-us/HT204087