Scott, while I cannot guarantee it's the best biography of Jack, the biog JACKIE ROBINSON, written by Arnold Rampersad, I found to be especially good. It was written in 1997, fifty years after Mr. Robinson broke major league baseball's "color barrier".
I would also highly recommend Roger Kahn's classic, THE BOYS OF SUMMER. Kahn covered the Brooklyn Dodgers during the 1952-3 seasons for the New York HERALD TRIBUNE. Roger got very close to Jack, and really understood him, whist Jack picked up on Roger's deep respect and sensitivity to what Jack was trying to accomplish. As a result, Jack opened up to Roger all the more. Kahn interviewed a good number of the Dodgers from the two years, but Kahn said more in the book on Jack than you'd find in most biographies of the man.
You'll find good first edition hard bounds on EBAY cheaply. Enjoy!
--- Brian Powell