Thank you for being specific as to what your issue is. Something you said is confusing however. You state that you used an Ethernet cable, but "Both computers indicate they were connected to my Network." When a direct wired connection is used, there is no network involved. While it is possible to use an Ethernet cable, I strongly suggest that you use a USB cable instead to connect the two computers together. It is much faster and the data being transferred is less likely to get corrupted.
As to your first question, yes, something was wrong. I have no way of knowing what, though. I think that you did not take the time to read and clearly understand what steps to follow. (I am sorry, I do not mean to be critical, only to be helpful.)
As to your second question, you saw that you were given some specific options as what to have transferred. I agree that it may not be best to transfer your applications. They can be newly installed on the new computer and then will be the most current version and will be "clean". You most likely will want to transfer your preferences and settings. It is not possible to select which files to transfer. It's all or none. If you select none, then you must manually copy them over.
Migration assistant is actually quite easy to use. Basically, to recap, the process is as follows.
You first begin by starting the process of setting up your new computer. You will be asked if you wish to transfer files. Respond YES and follow the instructions you will be given. Take the time to read and understand them.
You will be told to turn both computers on and activate Migration Assistant in the old computer.
The computers should be connected with a USB cable to facilitate the transfer. Wi-Fi is simply not suited for a transfer of so much data and corruption often results. Do not use it.
You will b given several options as to what to transfer. You will likely want to transfer your settings and preferences.
You can transfer all or none of your files. You do not have an option to select certain files to transfer. If you wish to do that, then do so manually.
The old computer's operating system will not be transferred.
Allow for up to an hour for the transfer process to complete once you start it.
Enjoy your new Mac.
I hope this is helpful. Good luck.