honestly, figuring out the order used to be a pain. The way I see it, you have two valid paths: publication order or in-universe chronological order. For a first-timer, I'd lean hard toward publication order because Vince Flynn's writing and the character's emotional arc just build better that way. Starting with 'American Assassin', the chronological prequel, actually robs some of the suspense from the early books like 'Transfer of Power' where you're learning who this guy is.
That said, if you're a chronology purist after your first read-through, the timeline starts with 'American Assassin', then 'Kill Shot', 'Transfer of Power', 'The Third Option', and so on. Kyle Mills continued the series after Flynn's passing, and those books slot into the timeline after 'The Last Man'. The Mills books maintain the tone fairly well, but you can feel a slight shift. My paperback copy of 'Order to Kill' is practically falling apart from rereads.
My advice? Grab 'Transfer of Power'. Dive into the original crisis. The later prequels hit differently when you already know where Mitch is headed.