A good question! Others will want to comment on this too. My suggestion, for what it's worth, is that if you're really going to get into Byzantine culture you need to do it their own way -- you need some background of classical Greek and Biblical Greek (but Biblical / New Testament Greek is really easy when you've done a bit of classical Greek).
But you can't manage without some modern Greek too. Anyway, anyone who studies classical Greek and doesn't want to know modern Greek is silly. In saying this I am criticising myself because I am still no good at modern Greek really. Now that my daughter lives in Greece I have taken a resolution to learn modern Greek properly at last.
i see...well thanks heaps.. i think there is a place nearby that teaches classical Greek. And i guess i could pick up a bit of modern greek as my brothers best friend is full on Greek and my brother speaks a bit.
well thanks for the suggestion mate ^^
I started with Biblical Greek. It ws the easiest to find materials. It was also the common language through about 225 - 250 AD so lots of the older Byzantine and late Roman Greek inscriptions actually use this form. Think of it as Shakpearian English, it is different but still understandable to the modern ear.
You can also order self-contained "Learn Greek" mateterials and lexicons through Chrsitian Book Stores at rather reasonable prices.