One of the most impressive items that I saw at SBL this year, and purchased there, is their Speak Koine Greek: A Conversational Phrasebook. It is exactly what it sounds like – a phrase book for ancient Koine that resembles the format and contents that you would expect if you’ve ever used any foreign language phrasebook before in your life.This sounds like fun. When I was in high school I taught myself Biblical Hebrew and New Testament Greek.* For Greek I used Clarence Hale's introductory grammar Lets Study Greek (and my copy had that same garish purple cover).
Its approach was not dissimilar to what James describes above. Rather than using passages from the New Testament, it gave the student progressively harder passages composed by the author in New Testament Greek. These were little stories with conversations and adventures. "Hi Peter." "Hi John." "How are you?" "I have a fever." "The merchant was a bad man." "The slave was wise and healed the little boy's fever." And so on. I can't find it right now, but I'm pretty sure I still have it around somewhere.
I don't know whether that is the best pedagogical approach for teaching an ancient language, but it worked for me in high school. By the time I finished the grammar I could read the New Testament in Greek reasonably well.
*Yes, I know. Nerd to infinity.