Marie, other thoughts....
Check out British Airways for their flash sales. (I think a lot of airlines have them now and again.) I got great, great RT fares (two years in a row) from BOS to FCO (layover in Heathrow.)
Of course, I don't know how much it is for them to fly from their home state. I prefer to book direct with the airline after I have done some checking around on other booking sites.
When you or they have narrowed down some hotel or hostel possibilities, ask if there is a discount if bill is paid in Euro at the end. Some may give a 10- to 15% discount. Also, have them ask in restaurants for the same. Sometimes, the waiter will offer a small discount if paid in (cash) Euro of course; especially the smaller, cozy-style (sit down) restaurants. "Check the bill and get a receipt if possible."
If they don't want to eat the table bread, have them tell the waiter not to cut and bring any to the table.
I prefer Pinot Grigio instead of House Wine. House wine is okay and not expensive; can be shared -- staff brings a carafe and glasses or, that was my experience when I had dinner with a friend in Rome. Every little Euro adds up or can be saved, lol.
There was one night, on my first trip, that I wanted a Panino. I went to the market, got one with Prosciutto and Cheese, a salad, dessert, and drank my bottled water. I walked to Piazza Navona. It was dark by then. I sat on one of the benches in the Piazza watching the World go by, enjoying my Panino and fixings, just getting lost in watching the Fountain I was near...
I also got a side treat...up a bit, In the distance, I heard the street musicians (I had stumbled upon one day at The Pantheon) playing their instruments, harmonizing with haunting vocals from the lead singer. It was wonderful and relaxing. I forgot about the time, lol.
Oh, and the "ride from the airport" to their hotel/hostel. An official White, Roma cab will cost 48€ (during regular day hours) I don't think they charge for luggage. I believe it is included. Best to check on that. So, for two peeps (when you break it down), it will be 24€ a piece -- private. http://www.adr.it/en/web/aeroporti-di-roma-en-/pax-fco-taxi#
I use a shared shuttle. I didn't mind. I usually got dropped off first since my hotel was near Termini.
Drivers were great and professional both times I used them; so far. For me, the first RT fare (FCO to Rome's Termini and vice versa) was about 50€ (so, 25€ coming and going) -- second time was less - the manager gave me a 5€ discount, lol. "Repeat customer." He remembered me from the year before!! Or so he said, LOL! Jokes aside, if I was traveling with another, I would take a taxi for two or three peeps.