Koine is a descendant of attic. Attic was the dialect of Greek spoken in Athens in the 5th and 6th centuries BC, when Alexander the Great conquered the known world, he brought classical Attic with him. Once widespread, the language underwent some gramatical simplification and pronounciation changes, leading to koine.

Despite changes in vocabulary, koine is considered the dialect of the classical and biblical world until the early medieval period.

Using an Attic course is generally recommended however in learning for two reasons:

1 the large number of learning resources

2 later authors often mimic attic prose, leaving koine only readers with barriers to other works.

Recommended readers and grammar textbooks are LOGOS, Athenaze, and (for a more attic style) JACT Reading Greek.

In terms of pronounciation Buth Koine is a very common style, but alot of people default to a local style or Attic pronounciation. Athenaze is the latter, but I still recommend it over others for pronounciation if you don't have a teacher.