To quote Fortson:
It is a remarkable fact that Greek has remained Greek over its 3300-year written history. Throughout this time, its dialects never developed into mutually incomprehensible languages, and are at all times recognizably woven out of the same linguistic fabric.
Resources for any dialect of Greek are to lesser or greater degree applicable to the rest, and indeed Biblical Greek is mostly just Classical Greek. Aside from the missing dual the only major differences in morphology I can think of off the top of my head are the third person plural of the imperatives. There are many other changes, but these are mostly shifts is class, e.g., Biblical Greek turns a lot of Classical Greek vocalic futures into sigmatic futures; that is to say, Biblical Greek has vocalic futures too, they're just rarer than in Classical Greek. I mostly read texts in Biblical Greek, and I always keep a copy of Smyth's Greek Grammar, which focuses on Ancient Greek, on hand, and it's as helpful for Biblical Greek as any book that's specifically about Koine.
Having said that, I don't know why you would study Biblical Greek if you aren't interested in the subject matter. There are plenty of resources for any dialect of Greek you want, and even the resources for Biblical Greek are often based on Ancient Greek. Case in point, William Mounce's Morphology of Biblical Greek can't go two pages without making a reference to Smyth. I just looked up a random page, and there were two references on that page alone.
I'd just focus on Modern Greek if I were you. Then later get a copy of Hardy Hansen's Greek: An Intensive Course or something.
"Hellenistic Koine" is more appropriate than "Biblical Greek", which seems to have been coined by scholars influenced by "Biblical Hebrew". The Hellenistic Koine language was much more than a religious language, so it can not be defined as "Biblical Greek".
Fair enough, but on account of its international spread the language changed a lot during the Koine era, and different regions, certainly outside of Greece, showed considerable variation. Biblical Greek simplifies things by not worrying about developments that never made it into the christian or Hellenistic jewish texts (particularly since early christian writers held the Septuagint, which is from the beginning of the Koine period, as a standard).