I'm a librarian and I have a request from a patron for books about the "quality of the Greek in the New Testament." He seems to think it's "actually quite poor" but I wonder if he's misconstruing the difference between Attic and Koine Greek?
Anyway, I think any book that was about how all the New Testament books were written and codified would satisfy him. The only book in the FAQ that I thought related to his question, A Brief Introduction to the New Testament, isn't in our system. If that's truly the best option, I'll ILL it for him.
It's actually quite difficult to isolate a book that only talks about the nature of the Greek language of the New Testament.
What I can tell you is that your patron is probably misled on the topic. We know that the NT was written in a kind of mid-range semi-literary Koine Greek. If one's standard for 'quality Greek' is based on Attic ideals, then Koine will always fall short, just as if today your ideal of 'good quality English writing' were based on Shakespeare, Bacon, and Marlowe.
Within its own mileiu, comparison with other Koine literature reveals that the NT is indeed 'literature', it's a body of carefully composed and written works, drawing a great deal on the literary tradition of the Old Testament, primarily in the Septuagint.
What your patron probably needs to read is a diachronic treatment of Greek language history. Anyway, some reading suggestions on the nature and type of Greek in the New Testament: