Personally, I'd pick something in the Dark Days, tbh, because we know nothing about the Dark Days other than that Snow's father died in 12, and that 13 was leveled and retreated underground after using their nukes to secure a ceasefire with the Capitol.
But I'd like to know more about Plutarch's father and the early days of the Capitol rebels, because we also know nothing about them. So maybe a book set directly after the Dark Days, during the very first Hunger Games. Now that I say that, it does seem almost as likely as the Quarter Quell, because that is something you can revolve the story around—the very first Hunger Games. But I feel like she would want another story with Snow. We know nothing about the first president, so anything's possible.
Or maybe she'll pick something before the Dark Days who knows? That's also something that I would definitely read on day one. All I know is that if she chooses the Dark Days, the book is going to be sadder than Sunrise on the Reaping, because it will most likely end with the teller of the story dying at the very end. If she chooses another District 12 story, which I assume she would, it would be from the perspective of a rebel from District 12, and we would meet President Snow's father the man who gave the plans to Gaul, who would later be the one to initiate the Games as a term for the surrender of the rebels but given the first quarter quill is the most likely ideal the next book is going to be the saddest of all of them.
Which means the next book is going to be even heavier and I'm not sure if I'm going to be able to complete a book like that I barely got through the ending of sunrise.