I'd recommend you listen to everything (i.e. all types of Orthodox Chant).
Greek Chant IS Byzantine Chant...(except when it's not). Byzantine Chant is the music of the Churches of Greece, Alexandria, Antioch, Constantinople, Jerusalem and also heavily used by the Churches of Albania, Bulgaria, Romania and Serbia (along with Slavic Chants). What I mean by not is that you will find some harmonized music labeled "Greek Chant" that is actually modern Russian Chant. This happens with some Carpatho-Russian Chants as well that are labeled "Bulgarian Chant". I think I was told the "why" some time ago, but forget, so I'll let someone else address that.