I was just at the beach in Fiumicino this week while seeing a friend off. The beaches are sandy and there are lots of shallow coves where kids of all ages were playing, including teenagers. We stayed at a great little B&B right on the seaside and had some great meals. The only downside is the usual Italian beach club scene - most of the beach side was occupied with the various clubs’ umbrellas. There were some free beaches, and if you were willing to rent an umbrella and loungers for the day from one of the clubs, it could be a feature not a bug. Had some great gelato too!
AFAIK, the route suggested above is the best way to get there - train or bus to the airport, then a short taxi ride to Fiumicino. I’m sure there are public buses too. A few cautions - first, the taxi lines at the airport do not offer taxis to Fiumicino, only to Rome. They don’t want the short trip after waiting for a fare. You have to call a car service from Fiumicino to come get you. Second, the official taxis are on strike anyway, so you need a car service.
If you are interested, I have the name of the B&B, a very prompt and reliable car service, and a great gelateria. I don’t know if this is the very best coastal beach near Rome, it’s the only one I’ve been to but we enjoyed it.