Ostiense or Tiburtina stations?

To a degree, it does not matter except for timing. From FCO you will take the regional train, FM1, which stops at both Ostiense and Tiburtina, with Ostiense being first. Tiburtina may have more services if you were looking to get a sandwich or snacks before catching the train, since you will be on Italo Treno and need to catch a specific train and departure, allow plenty of time to get off the plane, hit immigration, get to the FCO station, take the 45 minute or so train ride, get to your train, etc.

I agree, the station doesn't matter much. Be sure to give yourself plenty of time when booking the train tickets. You never know if your flight is going to be delayed and if you buy the reduced price tickets they may be worthless if you miss the train. You may want to consider buying tickets the day you land. Donna

The .Italotreno usually starts its journey at Ostiense, calling at Tiburtina after 20 minutes or so. The lounge upstairs at Tiburtina (near somewhere in the mid-teens of platform numbers and near the platform used (I seem to remember platform 16-ish) is quite nice (but has no toilets which are back down a couple of flights and around the corner) and provides free wifi. I've never seen the lounge at Ostiense.

Thanks you all for the valuable information. Our plane is scheduled to arrive at 9:55 and the train is at 12:50, so we may just wait to buy tickets until we arrive just in case our plane is late.