Homeric morphology and vocabulary would likely pose difficulties for someone whose experience of Greek has been limited to NT koine, but the syntax is easier than almost any other ancient Greek text. And, as C.S. Bartholomew notes, after about 1000 lines the difficulties iron themselves out and you pick up speed.
The Anabasis is the easiest Attic prose text I'm aware of--just for fun, I recently read the first four books (up to thalatta, thalatta!). It's more interesting than I had remembered it, and the narrative is livelier than Caesar, who is the Latin analogue, mainly because the Greeks with Xenophon actually find themselves in difficult situations--Caesar, in his telling at least, never econounters really serious obstacles.
Plato's Apology is a relatively easy text Attic text, and it's a foundational text of Western Civilization.
Speeches of Lysias are not too difficult, either, and I think they can be interesting for the light they shed on everyday Athenian life and society.
But if I were you, I'd go for the transcendent experience of reading Homer in the original--for me, at least, that has always been the most important (though by no means the only) reason to study ancient Greek. Brenner's Selection from the Iliad is a good place to start, but you may want to read more recent material about the mysterious origins of the poems, their background and history, their role in Greek civilization, etc.