If you think you'll make it by 6:30 (which should allow plenty of time) take the metro line to Ottaviano and wait for the hotel shuttle at a stop that I believe is on via Giulio Cesare (near no. 29, runs on the half hour). I'd check with the hotel on that.
Alternatively take the metro to Valle Aurelia, go briefly out of the station to the FR3 (no new ticket required) and go in direction of Viterbo, exiting at Gemelli. As you exit Gemelli station (go to the left), climb the stairs, turn left again (you'll see a supermarket across the street and an intersection straight ahead of you. At the intersection, turn left again, go less than a block, left again and you're at the Marriott Central Park. It's less than a 5 min. walk.
I just realized I'm assuming you're going to the Marriott Central Park. If you're going to Marriott Park Hotel, I can't help. If you're going to the Flora and want to take the metro, go to Barberini. Then it's a bit of a walk up the hill on Via Veneto to the end, where the Flora is located. If you have a lot of luggage, that could be difficult because it's an uphill trek.
And do buy a 3 or 7 day metro pass -- the cost savings may be limited depending on how often you use the hotel shuttle, but you don't have to constantly buy a new ticket.