I happen to be a huge fan of Bach's works... I actually have three different editions of his "complete works".
To make a smoother transition between the Beach Boys and Bach, I'd advise you to buy "Switched On Bach" by Wendy Carlos. Be sure to buy a CD or a vinyl with the original recordings (from around 1967/68/69... Can't remember), as there have been many re-recordings of poorer quality.
If you don't know what "Switched On Bach" is, it's some of the best-known Bach tunes played on a Moog synthetizer. And it's GREAT. Aerial. Lighter. Maybe more "accessible".
In the "Caroline, Now!" tribute CD, Brian stated that he loved this album, and that it could have been one of his inspirations for the "Love You" album!
I'd also recommend you the three "Brandeburg Concertos" (or "Concertos Brandebourgeois"), which are simply amazing.
(P.S. It seems that some classical music experts think that the "Goldberg Variations", along with some cello suites, may have been written by Bach's second wife, Anna Magdalena:
http://www.cbc.ca/arts/story/2006/04/24/bach-wife.html)