Is it quicker to use an ethernet connection between the two Macs?

dacadoyle wrote:

When using Migration assistant is it better to use an ethernet connection than wifi?

Yes, a direct Ethernet connection is slightly better than using Wi-FI.

If I don't have an external hard drive, what is the best way to go, aside from getting one going forward?

However using the old Mac's Time Machine is really the best and most reliable option.

Neither is recommended!!!

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 Yesand 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. 

Get one today!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! There is no reason not to and not doing so is risking losing all your data. Most experienced users on these forums use one of these https://eshop.macsales.com/shop/owc-mercury-elite-pro

NOTE the price on the 3TB model.