Grazie mille!
I'm landing on a Sunday morning at 7h so I am hoping there won't be much traffic but the Leonardo express sounds perfect.
I never check bags either - that's the problem I'm dealing with. Unless I check my roll aboard, I would have to take it into the city center with me.
Since my visit is very short, I don't know if I'll have time to get off the beaten path although that is usually the m.o. of my trips. Given time constrains, I'm less worried about dining than seeing things I've always wanted to see. I'm in Italy once or twice a year, I just have never (sadly) been to Rome.