I don't recommend a whole raft of programmes, but have been listening with great enjoyment over the last few days to this excellent series from 1974 presented by Bob Harris and recently repeated on BBC Radio 6. In fact, if you read this in time - ie sometime over the next seven days - then all or some of the programmes may still be available to listen on BBC iplayer. To listen, go here.
What makes the series so enjoyable is partly that there is time enough to stretch out: with six one hour programmes to take the story up to the mid seventies (I believe the ending was updated in 1976) there is time to hear interviewees at length and even to hear conflicting memories of key events from those involved. Additonally, Bob Harris is actively involved - he's doing at least some of the interviews. There is a tendency in otherwise excellent music documentaries these days for getting a big celebrity name to do the narration and it doesn't always work.
Also recommended, though I don't know whether it's been repeated on BBC Radio 6 or elsewhere in recent years, is The Rolling Stones Story, which was narrated by Alexis Korner. I was researching Brian Jones for a play some years back and heard this at the National Sound Archive. Now, Korner had a great radio voice but also, as you may well know, has more right than most to tell the Stones' story. And there was a great moment when, having described the death of Brian Jones (Korner had been there to offer support and encouragement in his final days), he simply played a gospel recording of This Little Light which he said Brian would have enjoyed.
To return to the Beach Boys, that spread of time also means you get to hear a fair amount of music - not just the Beach Boys, but snatches of doo wop and other surfin' music, etc. And there is an occasional healthy scepticism in Harris's narration. So if you like the Beach Boys, give it a go is my advice. No doubt there may be other concerns occupying you. But to hear those early songs again is a joy.