I don't know Greek, but I've had some experience learning ancient languages (Anglo-Saxon, specifically) and I tried to self-learn koine myself after university.
The only self-teaching program I am personally familiar with is Learn New Testament Greek by John Dobson. I worked through about 9 or 10 lessons before I had to stop, and much of what I learned I have still retained. After a few lessons about recognizing and pronouncing Greek, he gets right into the text - you're translating John 1 by about the second or third lesson. (Instant gratification is great when learning new skills!)
So from experience I can say that Dobson is very good for what it is - an inductive Greek grammar. You may wish to supplement, or follow him up, with a more traditional deductive grammar such as William Mounce's. Also, if you really want to achieve competence and fluency, I personally have my doubts that a self-learning program is truly an adequate substitute for academic study. I've seen some self-taught, self-proclaimed Greek "experts" spout all sorts of nonsense online. What it probably will do for you, however, is enable you to follow the discussions in exegetical commentaries - which I wished I was better at.