Like Michael Masiello said, no real obstacles: things are simpler. There will be fewer Attic futures and Attic second declensions. In fact, they were historically called Attic not because they were alien to Doric (Doric loved the “Attic” future), but because they were alien to Koine. So λαός, σκανδαλίσω, not λεώς, σκανδαλιῶ. Some Latin loan words, but you will recognise them from English anyway: κουστωδία, κεντυρίων. Some particles are moving towards Modern Greek, so their usage may surprise you: ἵνα for example is closer to a subjunctive marker then just a purposive.
I’d just jump in. If you find it too easy, I’ll point you in the direction of Nonnus’ Homeric paraphrase of the Gospel of John. 🙂