What do you want to accomplish?
Many people think starting with Homer First is the best approach. If you're just interested in studying Greek and learning over time then I'd suggest this. Clyde Pharr's textbook looks great. You get to read Homer quite early on. There are several points of merit to working Homeric, progressing to Attic then possibly dabbling in Koine\Hellenistic.
If you're just interested in reading a certain attic writer, then start there. Several People here reccomend John William White's Book.
If you're just interested in Reading New Testament, moving from Homer to attic prior to NT is probably the best approach, but staying away from the Bible for such a length of time would be a bit frustrating. I'd probably have done this if I hadn't spent so much time working exclusively through a few Koine Grammars.
For Koine, Samuel Green is probably my favorite old textbook. Armed with it and casting a healthy eye at Nunn's would do wonders.