If you learn Classical Greek you will be able to read and understand Koine Greek. If you learn only Koine Greek, if you should desire to also read Classical Greek, you will have a lot more problems. Koine Greek was the language of everyday people in the Mediterranean region following Alexander's Empire.
Classical Greek is generally that of the Athenians in their heyday (c. 500 B.C.--330 B.C.). From there you can branch out to read ionic Greek (the dialect that the Homeric Epics are composed in), Boeotian (the dialect of Pindar), Aeolic (the dialect of Sappho and Alcaeus) as well as several others. Classical Greek will have a lot more forms that you will generally not see in the Greek of the NT (e.g. the optative mood of verbs has only 3 appearances in the NT if memory serves). I would suggest you learn Classical Greek because then you will have a good grounding to expand more. If you should ever desire to read Byzantine Greek, Classical Greek is a must because the Byzantines saw themselves as the heirs of the Classical Tradition and wrote in styles that were reflective of that dialect. Anna Comnena's Alexiad, for instance, is filled with numerous classical quotes, particularly from the Athenian playwright, Sophocles, and she writes in a very stylized, high Greek that is reminiscent of Thucydides (one of the hardest Greek authors to read, imho).
So, go with Classical!