That's exactly what I did last year. The long term parking at the airport wasn't expensive and I avoided the hassle of driving in the city. I took the train/taxi combo to get to the hotel, but had a bit of a problem trying to find a taxi who would use the meter to drive the short distance to the hotel from the train station. The first few we tried wanted to charge us 25 Euros if I recall correctly. For the return trip we used one of the airport shuttle services advertised widely in Rome. They picked us up from the hotel in a van and took us to the airport and it actually cost less than the train/taxi combo.