The book, American Sniper has been a very successful Bestseller, but how would it appear as a visual?
If I were deciding how to interpret the book, American Sniper, I would most likely choose to make it a film, because it isn't at all very "cheery" like in a live musical, so eliminate the obvious. Now if American Sniper was made into a TV Series, it could be very successful. But if it were a TV Series, the audience would be left with many cliff hangers to deal with, which doesn't apply to the book, but more so applies to other books or comics like The Walking Dead. So, a film for American Sniper would be the best option.
Now, every film has a soundtrack, whether they film producers hire a composer, or just use popular songs. I believe, for American Sniper, that using popular songs (that apply and fit well with the book) would be the best option. To me, I'd add Linkin Park, kind of to fit the deployment theme, and then maybe some country artists to fit the main character's personality. The songs I'd stay away from are the disco/electronic-hip-hop songs, because they don't apply at all to the book.
Finally, the sets. American Sniper firsts take place, (not the prologue) in Texas, Chris Kyle's hometown to be exact. So the set might want to be somewhere in the southwestern United States, but then comes the hard part, making the sets for Bagdhad, etc, more thinking about the places Kyle goes into combat. For those parts, maybe make some minor small buildings for the sets, then greenscreen it in the back. Greenscreening is a very successful tool to help movies look like they are actually in the setting(s) in which the story takes place.
Some other additional decisions I'd have to make are casting, cuts, the epilogue, and more. I feel like at the end of the movie, I'd add a slide that honors Chris Kyle, who died 4 years ago, as well as the other US Military members who laid down their lives to protect our country. The casting would then be decided looking at actors/actresses' past movies they have worked on with the same, or similar tone that American Sniper is aiming for, a serious tone.
