Does where I actually pick up the tickets really matter?
I am not sure I understand your question. It doesn't make any difference if you use the auto machine or a ticket agent. The ticket is the same/ However, if going out of the country (Italy to Switzerland) than it becomes an international ticket and you will need to use an agent. Will want to see your passport.
My question is.....is it better to pick up the tickets from a machine or at the train station in person? Is one more convenient? I would prefer to speak to a person, but not if it is highly inconvenient. Thanks!
Are you asking about pre-ordered tickets??? I thought I answered the question about purchasing from a machine or person. Generally the line to purchase from a person is quite long in major terminals. The machines are straight forward and often speak better English than the ticket agent.
In Germany, regional day passes, such as Schönes-Wochenende- and Länder-Tickets are less expensive at ticket automats. For those tickets, German Rail charges an extra €2 at the counter for person-assisted service.
As for full fare Bahn tickets, you can get them either place. I find it more convenient and faster to use the automat. I would not call counter sales "highly" inconvenient, but there are often lines at the counter.
The only way you can judge convenience for you is to wait until you get to the station. You will see if there is a line of people at the window or at the machine. Then you decide. Otherwise, all things are equal.
However, if you want to ask questions of course you must go to the window.