The Affair, by Lee Child

Even though The Affair is the sixteenth Jack Reacher book in Lee Child's popular series, it is set early in the Reacher timeline, as his time of service in the Army is coming to an end.  Jack is sent to a tiny Mississippi town with an Army base nearby to investigate a murder.  Tasked with going in undercover, Reacher attempts to take on the role of a drifter.  He sets out with only the clothes on his back, no bag.  He discovers the wonder of the pocket toothbrush.  He begins his habit of buying new clothes and throwing away the dirty clothes.

Once in town, he's immediately made by the local sheriff, who is a former MP in the Marines.  She initially tells Reacher to get lost, but he quickly makes himself indispensable to the investigation (and doesn't take long getting the beautiful sheriff in bed).  Despite stonewalling and misinformation from the Army, Reacher eventually cracks the case.  As we've come to expect, Reacher is a one-man department of justice, doing things his way, figuring stuff out and getting the bad guys.

This isn't the earliest book in the Reacher chronology, but it's an origin story of sorts, establishing some of his habits and lifestyle and ending immediately before Killing Floor begins.  Besides buying his first pocket toothbrush, he also learns about Western Union's ability to get him cash wherever he is in the country and introducing the logic of throwing away dirty clothes rather than laundering them.  Lee Child fans will love this addition to the Reacher series more than most.