I would suggest starting with Ancient Rome and just continuing on from there, one book per year. That will get you through the last 4 books of 6. No need to try to squeeze all 6 in. Modern and American history is probably the most important for high school, and then when she graduates, you can begin over again with ancient history.
Or, if you want to begin with Early Modern and Modern history because of the elections, you could begin there and then just keep going. As long as you fit the modern books in somewhere when she’s in high school, I think you could pretty much do whatever you want.