From which airport?

ROME FIUMICINO AIRPORT (FCO)

From Roma Fiumicino, there are 2 different trains:

1. Leonardo Express, directly to Roma Termini. You can only use it with a 1st class pass. Otherwise, you need to buy a ticket.
2. Suburban trains to Roma Tiburtina (and further). These only have 2nd class and can also be used with a 2nd class pass.

So if i understand you right I can take the suburban train with an pass i buy from Interrail? 

Correct.

Thank you

If you ONLY do these travels, then a pass is likely a waste of money-even more if you are willing to use local=regionale treni in Toscane=short distance, low price. Teh superfast Frecce R→ F can book advance for lower price and these is also competition from Italo treni=takes no passes.

If you also plan to do other trips in other countries, then it might be more worth it