I listened to the audio book version of Mark Lewisohn's "Tune In". It's the Beatles story up until their first UK album is released. Lewisohn says it was about 10 years of research - the book has a lot of detail but carries the storylines forward in an interesting way. I think the Jackson "documentary" will be interesting because very little footage of the Beatles working in the studio has been made public.
I too was a big Tolkien fan in my youth who thought the LOTR movies focused too much on the battles and skipped many interesting parts of the story but overall was better than I thought it would be.