The list is organized by recommended reading order, but also tagged with the main characters who appear in the series and the order they were written (which isn't the same as the recommended reading order now that more of the books are done). You can choose either path, or you can start in the middle with whichever series looks most appealing - but if you don't read Forgotten Vengeance last in Phase 1 you might feel a little lost in the beginning.
NOTE: Both Forgotten Space and Forgotten Starship, which are listed under Phase Two, can also serve as an introduction to the Universe, as it features its own set of new characters. But if you're already reading the other books, I recommend not jumping ahead.
Whatever you choose, I truly hope you enjoy it!
Ideal Reading Order
Phase 1
FORGOTTEN VENGEANCE
Phase 1, Series 5, Sheriff Duke, Caleb Card, Nathan Stacker, Isaac Pine, Max
Phase 2
FORGOTTEN STARSHIP
Phase 2, Series 7, Joseph Cross, Preslan Juno, Tyson Grant, John Washington, Max