We got a taxi between 5 of us..........I think it cost us about 70 euro. The journey was just over half an hour. We were going to the train station area. There were plenty of taxi's there when we arrived which was about 12 at night.
We flew into Ciampino last year. There were loads of buses there that bring you as far as the central train station in Rome. I think it costs 10 or 15 euros for the return journey. Its a small airport and the buses are laid on to meet the Ryanair flights. Journey took about 45 minutes as far as I can remember.
Buses are laid on for all ryanair flights. Bus shuttle is slightly better value E6 each way. http://www.sitbusshuttle.it/ Terravision, which is the company that Ryanair use is E14 return. If your going during the day then you could get a local bus to the Metro. It takes about 15mins for about a euro and then the metro to the city centre for about E2. Enjoy Rome. Its beautiful.