The question that you haven't really specified is this: Which Greek language do you want to learn?
Attic Greek (spoken by Euripdes, etc.) and Koine Greek is about as different from Demotic (modern spoken Greek) as English is from Chaucer. (Try and read the Canterbury tales with no footnotes and you'll see what I mean).
Homeric Greek is even further removed from Attic Greek. The language of Homer was tonal, like Chinese.
My point here is this: If you, (like I did) take Ancient Greek and then think you're going to be able to converse with a yiayia (grandmother) after liturgy in a Greek Orthodox Church, then think again!
Here's a couple of links to show you what I'm talking about. First, a Web site where you can hear Ancient Greek as Homer spoke it:http://www.oeaw.ac.at/kal/agp/
Listen to that awhile and then compare it to what you hear on some modern Greek radio stations that you can hear over the Internet, here:http://www.e-radio.com.cy/
See what I mean? The two languages are very different in pronounciation. Plus, Modern Greek has a whole host of loanwords from Latin, French, Turkish and English. In the liturgy, (which uses Koine Greek), the priest at one point says "Tas thyras, tas thyras, en sophia proskomen!" (Which means "the doors, the doors, in Wisdom, let us attend!" But, by contrast, Modern Greek does not use the word "thyra" for door, but instead uses the word "porta" which was taken from Latin.
Hope that clears some things up.