I second Sandy's opinion. We went early (before we headed to the ship as we stayed the day before in Rome.) and we walked right in, no lines at all. On te way out there WAS a line to get in. But I would not have gone to Rome and not gone to see it. It is fascinating that they could build such a structure so long ago.
I doesn't take that long to see it and it is right across the street from the subway (metro) entrance so you wouldn't need to spend money on a guide to see it. (Maybe arrange to start with the private guide afterward???
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14, Freedom x 2 6/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013