His autobiography stops in 1760 which would be well before the War. However, it is free on Amazon for use on the Kindle, so you could read through it without expending any money. At the very least you will learn much more about the experiences that led him to be the elder statesman and force during the shaping of America. It does ramble a bit.
The Real Benjamin Franklin, is a very readable biography that does a good job of allowing Franklin’s words to speak for him rather than the author getting in the way. There are two parts to this book, the first section is the biography, the second part is a collection of his remarks. It allows you to read his own words, see how he thought, and yet have a very readable text.
Honestly, I think both are worth reading. I had my girls start out TRBF and then read his autobiography. Either way you will learn about who he really was.