Are you able to keep your carryon size luggage with you on the train from the Rome airport to the Termini station? Can you keep it at your feet or does it have to go in racks?
You can keep your carry-on with you on the train between the airport and Termini. The ride isn't very long. My sis and I were able to keep our carry-ons on the floor at our feet, but that was only because no one was sitting in the seats facing us. Maybe you could keep it on your lap if you can't keep it on the floor?
There are luggage racks above the seats, but they are very small...you may keep your luggage at your feet, or on an empty seat...based on how crowded the train is...if you are traveling 1st class, it's never a problem. We've even taken our bike cases on as luggage on several trains in Italy-never been a problem (they look like a suit case on wheels)
Sara and Ellen are right. You can keep your bags on the floor in front of you. Never let them out of your sight.
Someone may want to move them to sit down, but keep you hand on them and keep them close to you even if you have to place them on the seat between you.
I have found it convenient to keep bags at my feet. It discourages passengers from crowding into your seat. They will look elsewhere.
I wouldn't be too worried about having your luggage right by your side. I've made the trip many times and have usually just put my luggage at the end of the car (on the luggage racks provided) I'm riding in and kept an eye on it. The train only stops at the termini. Of course, I keep my backpack with all my important papers in my possession.