Best way to get from airport into Rome (Hotel Suisse)??

"Best" does have several meanings.

For my suggestion "Best" does not = Cheapest or quickest.
If you will be getting off an all night trans Atlantic flight my "best" will be the lowest stress while jet- lagged. Go to the taxi stand line and take a taxi. It is a fixed price ...last I heard it was 48 eruo for I think up to four people in the cab. (Others will confirm or correct these details.)
If Hotel Suisse is within the City of Rome walls these details will be in effect.

Thanks. Yes, I meant the least stressful!

Taxi, definitely, esp. since you will have bags. 48 euros total and you get dropped off right at the door to your hotel. Be sure to get one of the taxis in the official queue at FCO. Do NOT take a taxi from anyone who approaches you in the terminal.

The best way is always a car and driver. The man with a name on a card that will take your luggage and lead you to a nice limo.

Romecabs.com. We used them to get from FCO to Trastavere. It was a little more than a regular taxi (€55) but well worth it to have a driver take your bags and take you where you need to go.