There are at least two first class biographies of Woody Guthrie.

Woody Guthrie; A Life, by Joe Klein, was published in the early 1980s. So it's a little out of date.
Rambling Man, by Ed Cray. Published 2006, so it includes quite a lot of material which is not in Klein.

Both are important reads but, if you can only afford the one, I'd go for the Cray.

There is also Hard Travelin' by Robert Santelli and Emily Davidson. I've never seen this book, so I can't comment. Does anyone else know anything about it?