“Those who wish to cultivate intercourse with the living Greeks, — and there may be not a few in London, Liverpool, and elsewhere to whom this advantage is open, — should accustom themselves, in reading prose at least, to pronounce the vowels and diphthongs exactly as the modern Greeks do; a habit which will be of great use even to exact scholarship, as it is certain
that the so-called modem Greek pronunciation is in its main peculiarities as ancient at least as our earliest manuscripts, which contain not a few errors springing obviously from the ears of the transcribers having been habituated to the vocalization 30 characteristic of the present Romaic. The peculiarity of this Byzantine orthoepy, as we may perhaps most correctly call it, is the predominance of the slender sound of ee, which, besides the two cases of ι and ει given above, engrosses also the three sounds of η, οι and υ. That this predominance of one of the feeblest sounds in the scale is both a corruption and a deformity need scarcely be proved ; it ought to be remembered, however, that it is both an early and a characteristic corruption, and harmonizes completely with what Quinctilian tells us of the character of the Greek vocalization as opposed to Latin in his days: “quamquam iis major est GRACILITAS, nos tamen sumus FORTIORES."”
Greek and English dialogues for use in schools, John S. Blackie 1871
https://archive.org/details/greekandenglish00blacgoog
I could not have expressed it better, and what is even more remarkable the above quoted reflection is in the middle of the author’s preliminary remarks describing a pronunciation which is not the “modern” (or historical) pronunciation. This really is in line with the idea of how little important pronunciation is, as long as it is kept constant and the language is orally practiced. A great book recently published (and wholly in Greek, but for a Spanish introduction for the teacher and a grammar index at the end) includes a CD recording all lessons in both the historical and the Erasmian pronunciation, so users may choose the one of his personal preference (1). This is actually an extra merit of the author who has very well argued points against Erasmian pronunciation (2). Incredibly interesting are both Blackie’s and Rouse’s (3) reflections on ancient tongues and the teaching process in general in his Greek teaching books, both of which I propose to be included in the Textkit library. Much more on the teaching-learning process is available at Vivarium Novum (4), with a brilliant conference regarding both Latin and Greek teaching. While the speaker (A Miraglia) employs the Italian-ecclesiastic pronunciation it nevertheless absolutely nice and clear Latin easily understood -Orbergis gratia- even when this tongue has been learned with pronuntiatio restituta, again showing how it is a not such an important issue (5).
(1) (http://www.culturaclasica.com/lingualatina/linguagraeca.htm ivvox sample audios provided, no personal or commercial interest in it or in any other of the links I might have ever posted in the forum, disclosure included just in case… 
).
(2) http://aigialos.blogspot.com.es/2007/07/pronunciacin-erasmiana-no-gracias.html
(3) https://archive.org/details/AFirstGreekCourse
(4) https://vivariumnovum.it/risorse-didattiche/propria-formazione/storia-e-teoria-della-didattica
(5) https://www.youtube.com/watch?v=C4fhl74bC1A
Ὁμοίως χαίρω κἀγὼ σε γνωρίζων ὦ φίλε Μάρκε. Χαῖρε καὶ σύ, ὦ Σαῦλε,
Χαλεπὸν μὲν τὸ τὴν Ἑλληνικὴν φωνὴν γράφειν, ἡδονικὸν δέ. Εἰ γὰρ βουλόμεθα ἔν τε τῷ ἀναγιγνώσκειν καί ἐν τῷ γράφειν ταχύτεροι γίγνεσθαι δεῖ οὖν ἡμᾶς ἀλλήλοις ἀττικείζειν, ὡς ἑμοὶ δοκεῖ. Ταύτα ποιοῦντες ἡ μὲν ἡμῶν ἡδονὴ ταχέως αύξήσεται ἡ δὲ πόνος σαφῶς μειωθήσεται.
The idea of going from ancient to modern and back again is well developed at http://blogs.ua.es/santiago/category/recursos-griego-moderno/ with lots of links and suggestions for modern Greek learning. I started with the advanced One package which starts from scratch, beginning with alphabet.
http://www.greek123.com/learn-greek/product/advanced-beginners-reader-modern-greek
What a surprise it was for me when at page 135 I discovered that the everywhere modern Greek preposition στον, στη, στο came from εἰς + τόν, τήν, τό. I am sure if you throw yourself into it you are going to obtain an impressive benefit from the Νέα Ελληνικά adventure, ὦ Σαῦλε.
