Airports in Rome, Rome or Flumicino?????

Hi All!
Hope the New Year is turning out to be a beautiful one for all of you. I am planning a trip across Europe and as a start will be flying from Amsterdam to Rome. When I give Rome as the destination for checking the ticket prices, two airports' ames appear as Rome and Flumicino. Please let me know which one of them is nearer to the city center so that I may start my trip immediately on landing. Are these the international and domestic airport of Rome? As I am already in the EU, I wouldnt need the immigration check. So please let me know which one to book for in the light of the fact that I would start my site seeing trip immediately on landing.
Regards.
Travellingtechie!

And I again forgot one thing.....I would also like to know any websites which may provide me with good cheap air tickets for April
Regards.
Travellingtechie!

Leonardo Da Vinci-Fiumicino airport is the main international airport, and the AlItalia hub, and is about 20miles away from the city. There are regular trains which take about 30mins to the city.

Ciampino is the much older, smaller airport and now used by most of the low cost airlines, and it's much closer to the city. You either have to take a bus all the way (45mins to city) or to a metro station and change.

As travel times more or less even out, i'd be inclined to suggest a flight to the airport which has the cheapest prices, as opposed to a specific airport