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.
Some time ago I took a Bible survey taught by an excellent Theologian. He commented that there were other languages that were spoken at that time but that God selected greek because it was the most precise language of the area. We see that for instance in the word love. Unlike English or Hebrew Greek offers a precise word so there can be no mistake of the meaning
agapê (love, charity) and words derived from it
philia (friendship, love) and words derived from it
storgê (natural affection), only as astorgos (lacking natural affection) in Ro.1:31 and 2Tim.3:3.
I did not know you were Serbian Orthodox , I had the pleasure of attending Serbian Orthodox Vespers a time ago, I found them very beautiful and the people very warm and friendly.