Leonardo Express takes 32 minutes, cost is 14 euros per person.
Taxi from airport to center is fixed rate 50 euros- no tip needed. It takes about 30-40 minutes.
We prefer to just grab our bags, walk outside to taxi line and be on our way. Have your destination address on a piece of paper hand that and 50 euros to driver. Sit back and enjoy door to door service.
ONLY go to official taxi line, do not go with anyone along the way offering you a taxi.
If your hotel is close to train station- Termini- then Leonardo Express makes sense.
If you still need to get from Termini to your lodgings and need a taxi then taxi from airport might make more sense.
If you stay in historic center you can walk most anywhere in Rome, which is why we have never had need of bus or metro there. We did take a taxi to our early am Vatican tour and to/from train station when we had luggage- never more than about 10-12 euros.
Rome is very walkable, mostly flat and compact, and IMO walking is the best way to experience the city.
You cannot hail a taxi on the street, must get at an official taxi rank- which are located at every major site, train station, etc. Pretty easy or have your hotel call for one. Uber as we know it here does not exist in Rome- it is Uber Black- which is more expensive, more like a limo service.
Leonardo Express
https://leonardo-express.com/en/en-leonardo-express-tickets/
Taxis in Rome
https://www.romewise.com/taxi-in-rome.html
(Some info on this page is out of date- the fixed rate has increased- but in general it is helpful info)