Transportation from Fiumincino to Dei Borgia Hotel Rome

Guess it depends how much luggage you have. I think best would be:
Leonardo Express Airport Train from the airport which leaves every 30 minutes and stops at Termini Station (this takes 30 minutes)
From Termini Station it would be a 10 min walk approx. to your hotel.

You could add to the cost and convenience by taking a taxi from Termini to your hotel.
A taxi from the airport would be even more convenient but likely take longer depending on traffic than the express train and will definitely cost more.

Couple of things: if taking the train do not let anyone handle your bags or lend you a hand.
If taking a taxi from the airport, make sure it is a licensed taxi, plenty of gypsy cabs will be looking for rides inside and outside the airport and will give you a low fare to get you in the taxi that ends much higher when you are actually dropped off.

The best way is always a prearranged car and driver. Only way to go.

The fixed taxi rate is 48E for up to four passengers and luggage.

The Leonard Express is 14E and non-stop to Termini in about 30 minutes.

The FM10 train is 8E and makes three stops prior to Termini is 8E (I think) so it is about 45 minutes.

And a shuttle bus to Termini for 8E.

Pick your best.

Since you asked for the best way, consider a private car service. After a long flight, some jet lag, not being familiar with the area, there is nothing better than having your private driver meet you inside the terminal and whisk you to your hotel. No fending off the "outlaw" cabs, waiting in the regular taxi line, or just having a "lost" feeling. It is not the cheapest way, but it is definitely the best. We can not say enough good things about Rome Cabs. It is a private car service (not a cab company) but only cost about 10 Euro more than a regular taxi. We always use them and have always been very pleased. Go to romecabs.com and see what you think. We usually send an email and they answer us with a quote within 24 hours. You do have to pay cash (Euros) and the end of the journey but not in advance.