I'm starting now with Ἀγαμέμνος ὑπόθεσις! All in all the Greek of the hypothesis is quite straightforward. There's a couple of things I'm wondering about.
1) The word ὑπόθεσις - what does it mean exactly? Does is mean "subject of the play" (like LSJ II.3), or (not so likely, I think) "starting point" (LSJ IV.3). Or "summary" or maybe "introduction"?
2) The end of the hypothesis. Does πρῶτος here just mean that this year Aeschylus was first, that he won?
ἐδιδάχθη τὸ δρᾶμα ἐπὶ ἄρχοντος Φιλοκλέους Ὀλυμπιάδι πη ἔτει β. πρῶτος Αἰσχύλος Ἁγαμέμνονι Χοηφόροις Εὐμενίσι Πρωτεῖ σατυρικῶι.
"The drama was produced during the archonship of Philokleos in the second year of the 88th Olympiad. The winner [was] Aeschylus with Agamemnon, Choephoroi, Eumenides [and] the satyrplay Proteus."
Is this correct?