Any suggestions would be appreciated
Of course, first question is define best - cheapest, quickest, fastest, most convenient???????
There's a train that runs about twice an hour from the airport (same station as Leonardo Express) to Tiburtina. Takes about 40 minutes and costs about 8 euro.
We took the train that Frank described and had no problem. We did have a slight problem finding the bus station. We were taking the bus to Siena and the station is just a parking lot with some small offices for the bus companies and even though we had seen it on google maps it was a bit confusing in person.