You are probably carrying too much for conveniently using the trains on this short trip. See the luggage section of http://tinyurl.com/3f9cmfh. You are also probably trying to see too much in a week. Vincenz?

The Leonardo Express from Rome's main airport is a dedicated airport train that goes non-stop to Rome Centrale station and thus has plenty of room for luggage even though it is not a deluxe train at all but always when I have taken it there was lots of room for luggage right by your seat - on the floor for example.

There are regional trains from the airport as well but these do not go to Centrale but to other secondary stations like Roma Ostiense and Rome Tiburtina and others. They are much cheaper but take much longer and can get very crowded IME.

The Leonardo is a regional train and travel time (speed?) is about the same as the FR1. They just go to different stations. You can go from the airport to Rome Trastevere in 25 minutes on the FR1 and they run every 15 minutes (Leonardo runs every 30 minutes).

I haven't been on the new Leonardo trains that were put into service this past year. They have more luggage space, but less seating so you might be standing for your ride.

****train will accommodate 690 passengers - only has 280 seats***

Regarding the Leonardo train Rome to airport. I had arrived back in Rome from Milan in preparation for flight home from Rome. Since I am somewhat disabled I immediately went to the platform for the Leonardo trains to see if I could manage my luggage here later that day. I discovered that every second train was level with the platform and every other involved stairs. After storing my luggage downstairs I then purchased a ticket from the ticket machine (avoided an enormous queue!) I had a final wander around Rome, collected my luggage, waited for a "staired train" to come and go, then validated my ticket and went down the far end of the platform. Along came a train level to the platform, rolled on my luggage, sat down - easy, easy.
PS This was 27 June 2012.

I assume the trains with the level boarding were the new trains kybourbon talks about and the ones with stepped the older regional trains she mentions. By 'dedicated airport' train I meant a train that goes non-stop from the airport to Termini station as opposed to other regional trains that serve the airport but stop a lot and do not go to the central main Rome station, Termini - yet the stopping train may be better for folks who say want to go to place like Travestere station if their hotel is near there.

2012 moving - I believe Trenitalia is still running old trains along with the newer trains on the FCO/Rome run. For people with mobility issues, the first car behind the engine (or perhaps it's actually part of the engine car?) on the old trains doesn't have steps, but the rest of the cars have steps. If you board there, you have a compartment with seating, but as you head back in the train, you would encounter steps again to access the rest of the car/train.

kybourbon
It's good to know that there is some mobility access on the older stepped trains Rome Termini/FCO run. I didn't notice that. The trains were very crowded and seating was a necessity for me. This prompted me to wait down the end furthest from the station entry.