The Last of the Wine!!
or you can do a poll; I had thought that reading them in the order of the dates of the novels would be best...and if you did that The King Must Die would be the first...
in order by the dates of the events in each
The King Must Die - Theseus
The Bull From the Sea - a continuation of The King Must die
The Praise Singer - Aristigieton and Harmodias
The Last of the Wine - Socrates and the Spartan war
The Mask of Apollo - Plato
Fire From Heaven - Alexander the Great's childhood to ascension
The Persian Boy - Alexander's reign
Funeral Games - events immediately following his death
and she has a novel set during World War 1 "The Charioteer"