There are at least 3 factors you will have to take into consideration, 1) will your flight arrive on time??? During the summer months (or really at any time) you could have delays on take off, which would then alter your arrival time. 2) as others have mentioned, will you be checking luggage?--and then have to wait for it to arrive, before going thru customs 3) the train from the airport to Termini arrives at the far end of the terminal in Rome and it can be quite a walk to the main part of the station. That said, I would go for the 9:45am train and if you miss it, just change your ticket for the next one. Worst case, you won't be able to get on the next one, and might have to wait for an available train. In that case, store your bags and walk around Rome until your train's time.