Confusion about the order is super common because of the way it's published. You've got the original series timeline, which is different from the publication order for the first few books. 'Killing Floor' is the first novel Lee Child wrote, so that's your true starting point. But chronologically, 'The Enemy' is a prequel set when Reacher's still in the Army. My advice? Go with publication order. You meet him as a drifter right away, and the flashbacks in later books fill in the backstory more effectively. Starting with the prequel first kinda ruins the mystery of his past. The publication order is the way the author intended the character to be revealed to readers.
After the first dozen or so, they're mostly standalone adventures anyway, so order matters less.
You guys are overcomplicating this. It's not a continuity-heavy series. It's a vibe. Find the vibe. For me, the vibe is a diner, a coffee, a quiet stranger, and a whole lot of impending violence. Which book has that? All of them. So close your eyes and pick.
The co-written books with Andrew Child (from 'The Sentinel' onward) are part of the publication order, full stop. Whether you enjoy them as much is a separate debate. But for the purpose of 'correct order,' they are #25 and #26. Andrew eventually took over fully, so this is the new era.
If you're a completionist, you read them. If you're a purist who thinks Lee Child's voice is irreplaceable, you might stop at 'Blue Moon'. But the question was about order, not quality. The order includes them.
I'm a mood reader, so I sometimes rebel against strict order. Some days I want a snowy thriller ('61 Hours'), other days I want a Florida noir ('Tripwire'). The series has a setting and tone for every mood. While I generally advocate for order, I also think it's okay to let your mood guide you, as long as you've read the first three to five to get established. Once you know Reacher, you can hop around based on the weather outside. It's a fun way to engage with the series on a different level. Match the book's atmosphere to your own.