Unless you're a member of the beach clubs there, don't count on getting in. It's a members only area during the summer.
As a teen I'd try to get to the jetty by walking the beach.... only to be turned around by security.
After the clubs close for the season, they sell fishing permits.... I think they go on sale October 1st.
You can fish the surf, the jetty or the inlet. Watch the inlet side, some spots have steep dropoffs.