Maybe it wouldn’t help you to start by yourself and be in conflict with the method of your school.
If you were going to study by yourself, then you should learn the dialect of the author you are interested in.
If you were interested not in an author, but in the language itself, you should learn the whole development of the language, all the three main dialects (i.e. Homeric, Platonic and Modern Greek).

As for your main question, learning modern Greek would give you the vocabulary and many grammatical and syntactical elements. But there are also differences, especially in the inflection. There are more differences between Homeric and Platonic Greek, than between modern English and Shakespearean English, and the same is true about modern Greek and each of the other dialects.

Whatever start you might decide, it’s a difficult course. Think carefully about the purpose of your studying.

Think of it as knowing a man. Would you know him easier if you started from an earlier or from a later age of his? Each age has its own difficulty, earlier ages foreshadow later ones, the later are more experienced, each one has, in this or that form of beauty, the worth of the whole man. If he is a great man, he has a great childhood and a great old age. If he is not a great man, none of his ages is great. Therefore, start according to your taste from what now seems to give you more joy and meaning, letting your thinking open to acquire more in the course of time – and never, never, follow this study in order to become an expert, a ‘professional’, a person who is expert in a small area, having lost all the treasures elsewhere. Study to be excited, not ‘informed’.

I really like Nikolaus post ... kudos!

I think many people are willing to accept a more simple approach, even if it is a little less accurate. They have enough at hand and mind trying to read the language very well. And if the more complex approaches to the sounds have inaccuracies too, at least the simplified ones have the virtue of simplicity. Just some thoughts.

Can anyone help me in locating and downloading Greek audio files [at least reading of passages of the NT by a native Greek]? I failed to obtain the late Mr. Zodhiates reading from First John as recommended elsewhere on this forum. I like what George says: "Study to be excited; not informed." At 50, I suddenly [from out of the blue] have this deep burning desire to learn Greek and I think to myself as to why I hadn't thought of it earlier! I had read about Homer and all the other philosophers and some of their works. Just think how exciting it would be to read/understand the New Testament and works of the Greek writers in the original language! So much to learn, so little time. I've really squandered it, haven't I? Now that I've learned O Αλφαβητος and as Greek words keep popping up in my head searching for meanings, I am excited by the prospect of floating in the vast ocean of Greek literature, both ancient and modern, and absorb the wisdom contained therein. What a prospect!! Therefore, the audio files assume great importance - to serve as vessels - to navigate in this ocean. Any help from any quarter would be most welcome and gratefully accepted.