You sound like you will be more than a little nervous about everything. With that in mind, I would have a couple of other suggestions. While it is nice to have everything exactly planned out, you will need to relax and develop some flexibility because it WILL NOT go as smooth as you want it to go. And remember it is Italy.
I would get at least a 100 Euro at your local bank or even a currency exchange at your departure airport. Finding an ATM is one less thing to worry about. And, my general experience is that ATMs are not as frequent or as easy to find at the airport as some claim.
Everything is in English more or less. But sometimes the English phrase is not one you are accustom to seeing. WC is the big one. That is Water Closet in English and restroom for Americans. I also do not find WC as easy to find in European airports as American airports. So watch for the signs. Can be downstairs, down long hallways, etc. Also the signage will make heavy use of the international symbols for various functions. Everyone you encounter will speak enough English to understand your question and point in the right direction. Don't be afraid to ask.
In my opinion the most important thing to know about your train ticket is your train number. It will be posted on the departure board. The last stop of your train sometimes is confusion but the train number is solid. Your train's platform will be posted on the board about 30 minutes prior to departure but it can be as late as 10 minutes. Second, don't be too eager to get to the platform because the platform number can be changed at the last minute. Will not happen often but it can happen. Yes, they will make an announcement but you will never understand it. However, if a lot of people around you start moving in a new direction, then ask someone because they understood the announcement. We generally hang around in sight of the board at the head of the platform until about ten minutes prior when move down the platform.
Ken and others are correct. Do not buy your ticket ahead of time. Assuming you are on a direct flight from the US, immigration could take anywhere from 15 mins to two hours. With customs just walk through the green door - nothing to declare.
I am troubled by your comment about a large suitcase. Just how large is large? If it is much bigger than a carryon size bag then it probably will NOT fit on the overhead rack. May have to put in the luggage storage area near the entrance to the train car. If you have a large, heavy suitcase, that just adds to your potential problems all along the trip. Get lighter. No reason you cannot fit in a carryon size bag.
Carry two debit cards tied to two different accounts just in the unlikely event that one doesn't work. We have been dependent on ATM cards only for the past 18+ years and have never had a problem but I still carry two cards. Also use both cards the first week just to make sure both are working. I am sure you know to inform your card issuers' fraud department of your travel plans.
You need to prepare for the unexpected so nothing is a shock.