Well, Classical Greek can be rather helpful. Yes, Byzantine Greek is rather removed from Ancient Greek but a) Greek goes from more complex to more analytical as the centuries go by, so, by knowing ancient Greek, you pretty much are going from more difficult to easier.
b) A great many byzantine writers actually wrote (more or less successfully) in Attic Greek. Some of the best works of the Byzantine era are written in Attic Greek.
c) Pronunciation-wise (if, that is, you are interested in pronunciation) Koine Greek and Byzantine Greek (well, most of the Byzantine period that is; we are
talking about 1000 years give or take a few) are quite close.
Since Byzantine Greek is sort of in the middle, modern Greek (my rant about my own language needing a "modern" before it can wait for another time
) can be really helpful too.
Oh, and by the way, if you know some basic Latin that won't hurt either