The practice today is to translate everything, from Homer to Euripides to the New Testament, into a clear contemporary English. But this has the effect of flattening out the respective historical and linguistic idioms of the texts concerned. So here's what to do: pick a date as a notional 'contemporary' (let's say, first century AD). Then assemble an anthology of Greek Literature in English. Translate the Homer and Hesiod into Chaucerian English; translate the Aeschylus, Sophocles, Euripides and Aristophanes into Elizabethan English; translate passages from the N.T. and Lucian's novels into contemporary English.
There would be plenty of scope for individual variation to reflect the particular styles of individual authors (Sophocles could be rendered Shakespearian, Aristophanes as Jonsonian comedy, Plato translated into the style of Francis Bacon and so on); and writers from other periods could be slotted into other periods: Apollonius Rhodius translated with Shelleyan flourishes, for instance.
It would be a winner.