The single best Greek resource for a beginner is Clyde Pharr's Homeric Greek. The original is in the public domain, but the book is also available in multiple contemporary revisions. Paula Debnar's 2012 edition is the best of these, containing many additional exercises and a more helpful appendix.

Even if you plan to read the New Testament exclusively, it is important to start with Homer. Doing so acquaints you with rare and older constructions like the dual form of the noun and uncontracted verbs. Attic Greek writers quote Homer enough to make a good understanding of the Iliad and Odyssey essential. Yet reading Homer is a joy in itself.

Passing from Homeric Greek, which takes one through the often complicated grammar of Iliad I, you should press on to the remaining 23 books. Get an edition that helps you, but not too much. Do not use a Loeb, but rather something like the orange student editions published by the Oxford University Press. After the Iliad, you can choose to read the Odyssey or lighter Homeric works like the Batrachomyomachia.

After your study of Homer, you will have the grueling but rewarding task of learning the differences between Homeric and Attic Greek. Learning complex forms is much easier for someone who has read Homer first and wants to read Plato than someone who has read Plato first and wants to read Homer. For this, spending time with Smyth's Greek Grammar is vital. Better still, look for a textbook on Attic Greek for intermediate readers. Louise Pratt's Eros at the Banquet is the best of these, and takes the same approach to the Symposium as Pharr does to the Iliad.

After that, you can read what you want. You will never stop consulting grammars, and you will never feel as though you really understand the language. Yet you will be reading Greek.