If money is no object/time is an issue, obviously taxi or some kind of chartered tour would be the best option.
You can, however, also get to the beach using public transportation. The Metrolink (commuter rail), which has a station in Anaheim right in front of Angel Stadium, will take you right to the San Clemente beach. On the weekends, there is a Metrolink station that literally drops you right on the San Clemente pier. During the week you would get off at the other San Clemente station, which is still right on the beach (just at the north end rather than the middle of the beach)
You can also take Metrolink the opposite direction, terminate at Los Angeles Union Station, and you can get to Long Beach using the light rail from here. This is much closer than San Clemente but requires you to transfer a few times (whereas Anaheim->San Clemente is a straight shot on the Metrolink). You'd transfer from Metrolink to Red Line Subway at Union Station, and then Red Line Subway to Blue Line Light Rail at Metro Center.
Both options are economical.
Metrolink website:
metrolinktrains.com/routes/
Info on the Metrolink station in relation to
Disneyland.
mousesavers.com/transportation-for-disney-vacations/trains-to-disney-world-and-disneyland/#dl