Without blinking an eye, I would save the Batrachomyomachy. That's the culminating point of the whole Greek civilisation. And if were allowed to, I would also save Aristophanes' Frogs, or at least my favourite line. Brekekekex koax koax!
Joking aside, I'm glad 2099 is still far away, because at present I feel totally underqualified. Homer would be the obvious choice, but I fear the Preservation Board will not be lenient if I save something someone else will have already saved. For the rest of Greek literature, I really have not read enough to make an informed decision... An obvious choice would be Plato, but frankly I don't understand Plato well enough to explain my choice to the Board. "Someone said that that Plato is, err, like, the foundation of the Western Civilization" – that doesn't sound very convincing. I'll be only in my 119th year then, and that's much too young to die. Aeschylus? Sophocles? Same thing. How would I justify choosing, say, Agamemnon? I mean, I've read it, but what was it about? The Board is going to ask me that, and I will not know the answer. Euripides? They'll ask me why the hell I saved Euripides and not Aeschylus or Sophocles – come to think about it, probably Scribo will be a member of the Board, and he'll be very, very pissed off at me for choosing Euripides!
No, if I want to save my dear life, it has to be something funny. Everybody has a sense of humour, or everybody at least pretends to. I will win over the Preservation Board by choosing something funny. The obvious choice is Aristophanes. How many plays was I allowed to take? Frogs is my favourite (but I haven't read all Aristophanes), but pointless without Euripides or Aeschylus. Ekklesiazousai is probably a good choice, it's very funny, it's has some information on the Athenian democratic system, it presents a mock-Utopia that goes awry (but alas, we won't have Plato to compare) and of course, it's about the relationship between men and women – and that's universal.