Thanks for the update. I just did a trial request for a transfer. Rometaxi.com quoted me €65 for a transfer from Fiumicino to central Rome. Romeshuttlelimousine offered me a "discounted" fare of €51, which I assume everyone gets, because they didn't ask me the date or time of day.

The standard official taxi costs €50.

€51 would basically be equal the cab fare. So that's not bad.

The cost for airportshuttle.it is E44 for two people, so that is cheaper than a taxi, as well as far more convenient. As I noted above, they also will be there when you come out, no going somewhere to find a taxi.

You're getting all sorts of advice here so probably more confusing then ever.

here is some more confusion

Getting through the rome airport was super simple for us. One of the first things you'll see is big big signs pointing to the taxi stand. We used many taxis while in Rome (although not from the airport as we picked up a rental car) and they were all good, clean, new. A taxi will have the regulated fixed price for transfers to the city centre on the side of the car (car door). It's a large sign with large print so you can clearly see what the cost will be. You can therefore take the taxi with confidence on the price and also that it is licensed. As per a previous post don't even look at anyone approaching you to see if you'd like a taxi.... just talk to the taxi stand clearly identifiable. It's super easy and safe.
We also found most drivers had some English ability.

Train is good
shuttle bus is good
taxi is good
private transfer is good

Go with how you like to travel..... it's all good

One more tip which I think you'll love
You can use UBER to choose between a private black car (so this would typically be a Mercedes Benz and many times the driver was wearing a suit) or a taxi cab. The cost of the black car is only marginally more than a taxi cab and the uber app will show you so you know what to expect.
uber is new to Italy so not every taxi driver is using it. But I used uber for taxis every time i used a taxi and I never waited very long.

One last point to clarify a previous point about transport.
My previous post said it would take up to an hour to get to the city..... I may have been more correct to say that it'll usually take between 35 to 60 minutes to get into the city centre depending on traffic conditions. I don't know why being more correct is important to some people on this forum but there you go. Hopefully this 25 minute range of times will not send anyone into a mental rage and can be a guideline to help you plan

The key thing with that guideline is that whichever way you go that general time frame will apply. Of course, any form of transport that is shared will cost less but take more time so that's something to consider too depending on your priorities.


Also, you asked about where to stay.....
When I did my research I kept reading about how this place or that is only a half hour walk to all the sites blah blah blah.
when I mapped it all out i found that if your plan is to walk everywhere then regardless of where you stay you'll walk a lot. You can walk a mile or 2 just in any single main site..... then walking to the next site etc it all adds up. Our biggest day was 12 MILES. We never did a day less than 5 and that's because we either did a small relaxing day or used taxis.
in my mind there are 4 main areas to focus your walking tour of Rome.... or 5 if you don't include the Jewish quarter into one or more of those 4 areas. From that perspective you can locate in the middle of any 2 of those areas but only 2.... which means either long walks to the others or taking a taxi or some other means.
buses and trams are excellent options..... i just prefer to spend the money and taxi it.

All suggestions offered to you so far are excellent. I agree with them all.
the only reason why I suggest a focus on the Spanish steps and the trevi fountain is because of my personality type. I prefer to see these iconic sites and to photograph them without people. I like having things to myself or close to it. So my advice is to go to the trevi fountain in the early dawn light or even before when it's still dark then go to the Spanish steps... spend time up and down the steps mostly by yourself and capture the sunlight as it first touches the top of the steps. It's peaceful and beautiful. Then to by taxi.... and I mean by taxi.... to be first in line to enter into either the basilica or the Sistine chapel..... go straight to one of those two places and then go back through to see the rest of the galleries after....
NOTE the basilica is closed Wednesday mornings.
the Sistine chapel is NOT terrible when it's crowded as you have to look up anyway so no one is in your way BUT within the first half hour or so it's still kind of peaceful. Later in the day it's noisy .... still wonderful to see but not peaceful if that's important to you. Oh.... the crowds are long so being the first in is worth it just for time management purposes. You'll see more of Rome in less days if you take this advice

absolutely not in my budget 🔨

I will soon be in Rome for the first time in a few years. I was shocked at the increase in hotel prices.