Like everyone else has said, German, German, German!
As a non-romance language, Latin gives you absolutely ZERO help on the vocab/grammar front. French, Italian, hell, even Spanish, definitely benefit from your Latin skills. Also, while some schools offer "French for Reading" courses, I've never seen one for German. Every grad program I've ever seen REQUIRES a German exam. Most require two, with French, Italian, or possibly modern Greek as the second option. A few programs I've seen require all three (minus the modern Greek).
But if you plan to work on Greek things, it'd probably behoove you to pick up the modern Greek as well. Especially if you plan to study/excavate in Greece at all. Much like Romanists tend to pick of Italian if they plan to study/excavate in Italy.
Seriously though, German. It can really kick your arse if you try that one without formal classwork.