I am Serbian. Kolokotronis is your resident Greek expert. That being said, I would add that God chose Greek for both the New and Old Testament for His New Covenant. The Gospels refer to verses from the Septuagint (LXX), remember?
I am not sure how precise the language is. But it is liturgical. In other words, it is capable of expressing divine concepts unlike ordinary vernacular. Thus, Latin had to develop into a liturgical language and Church Slavonic was specifically developed by SS Cyrill and Methodius as a liturgical language.
From what I know of Slavonic, it is capable of forming intricate concepts that correspond word-by-word, and grammatically, tense-by-tense, to the Greek original.