You've got tons of options.
The LIRR has a Beach Getaways Page with ticketing and timetable options for a variety of the simplest options; The best part is that many of these include beach passes or related bus tickets in a package price, saving you some money.
Long Beach is definitely the easiest, and probably my favorite. If you want a beach that has a bit more of an 'in town' flavor, with nearby bars and restaurants, it's the clear best choice.
Jones Beach and Robert Moses are both in state parks; the former is more developed, and tends to be a bit more crowded, but, has better facilities. It's also closer, and home to more events, thanks to the presence of the amphitheatre.
The various Fire Island options will, of course, take you much longer to get to, but will definitely provide different beach experiences, and fewer people around once you get there.
You can get to just about any beach on LI through a combination of LIRR and a single bus trip though, so if there's one in particular you'd like to target, you should have no trouble getting there.
And keep in mind that if you're looking for a weekend getaway, the LIRR offers it's weekly Cannonball service on Friday afternoons eastbound and Sunday evenings westbound - nonstop service from Penn Station to the Hamptons/Montauk in 90 minutes.