I consider the best Houdini biography to be Houdini!!! The Career of Ehrich Weiss by Kenneth Silverman. For me it's the book that best succeeds in separating fact from fiction. Published in 1996, it is now out of print, but you can still find copies on Amazon at reasonable prices. So if you want to go beyond the movie get into the real life of Houdini, start your journey right here.
Below are links to posts I've made discussing the contents and merits of the other major biographies of Houdini:
"This book is full of lies" (Houdini His Life Story)
The gateway biography (Harry Houdini Magician Extraordinary)
The first great Houdini biography (Houdini The Man Who Walked Through Walls)
An alternative gateway (Houdini Master of Escape)
The textbook (Houdini The Untold Story)
If there's another Houdini book that you feel is even better than Silverman, please share your candidate for Best Houdini Bio in the Comments below.