Getting there...

Assisi by train is easy. From FCO take the Leonardo Express to Roma Termini. From there you take the Trenitalia directly to Assisi. It's about a 2+ hour trip. The trains are frequent enough that you won't be standing around too very long in Termini.

Take the train. Depending on when you land, get through passport control, train to Rome (could be either Termini or Tiburtina stations). then trains with another connection to Assisi station, then bus or taxi to your lodging.

Just wondering - is there any reason to book in advance train tickets?

No, these are all regional trains, always the same price, no seat reservations available. No advantage at all (and some disadvantages) to booking in advance.

Thanks Robert and Sam. I didn't think it would be much of an issue and you have confirmed it. Highly appreciated!

If possible, can you come in a day earlier? If your flight gets canceled or you have a major delay, you may have difficulties. Sadly, with the jet fuel issues, flight problems seem to be increasing. Many carriers only have a few flights a day, and if your flight gets canceled, it's many hours before another flight is scheduled, which might have available seats. We once spent 24 hours in Chicago when our connection to Zurich was completely canceled. It happens.
But I'm wishing you good luck and safe travels.

Hi Woody, yes, there’s a regionale train from Rome to Assisi. But, there’s some maintenance on the line, so I took the Frecciarossa fast train to Florence & then the regionale south that goes south along Perugia, etc. I had a ticket for the regionale from Rome, but the bus connection wasn’t communicating & we sat on that train for a long time, so I went with Plan B. For a wedding, I’d take the more dependable route, even though it’s longer.

there’s some maintenance on the line

No, there are no maintenance works planned after June 13. And anyway during the works you were supposed to transfer to a substitute bus in Terni, not in Rome.