Hi Springhill, How about Theseus, conqueror of the Minotaur and King of Athens? If he'll do, you might enjoy "The King Must Die" and "The Bull from the Sea", by Mary Renault. She's also written a couple of novels set in classical Greece, both centred on Athens, a trilogy around Alexander the Great, and an utterly brilliant fictional life of the poet Simonides, who lived on the edge of the transition from oral to written poetry.
If you're more interested in original sources, have a go at the plays, especially by Sophocles and Euripedes. Classical, hellenistic, and Roman culture was all infused with Homer, and our versions of the myths - or histories - come from all of them.
One thing I find very important is to read more than one translation of everything. Mary Renault comments in an afterword to one of the Alexander books that "the moral reflexes of the world have changed". I think she's right about that, and it makes translation tricky. Then we have the additional complication that some of the translations from the 19th century are still widely used, and our own language has changed on us.
Have fun.
Ghoti