We did 4 days pre-tour in Rome, although we had been there before. We flew out of Naples the day after the tour ended for a back to back RS Best of Greece tour.
How many days pre-tour depends on what you want to see in Rome. Research it, decide what you want to see and then plot it out on a daily schedule and that will tell you how many days you need pre-tour.
FWIW, since we had been to Rome before, we spent our four days with a tour of the Domus Aureas, an underground tour of the excavations at Piazza Navona and the fountains of Piazza Navona, a Vespa Sidecar tour (highly recommended if you don't have much time to visit everything! This tour will drive by and briefly stop at important sites in Rome) a second visit to the Villa Borghese museum, a visit to see the Turtle Fountain in the Rome neighborhood of Sant Angelo???, an evening food tour in the Trastevere neighborhood, the Cat sanctuary at Torre Argentina (now open to the public and the site of the murder of Julius Caesar), the Pantheon (again) and Trevi Fountain (again) and a visit to Castel Sant Angelo and the Villa Farnesina, with many gelato stops.
The RS tour does NOT visit the Coluseem or the Forum, so you book a day on your pre-tour to visit that. Visit the catacombs along the Appian Way. RS also does not visit the Vatican or the Vatican Museum, so you'll want to book a day for that pre-tour.
RS tours stay in Trastevere and we liked that area also, so I recommend finding a hotel in this neighborhood, if you don't have a favorite area.