My suggestion is a question: why do you want to study Greek (or Latin)? What is it that you expect from this studying? Objective criteria, such as the antiquity or superiority of Greek, can not be your motivation, if, e.g., you are interested in understanding the Latin-speaking Fathers of the Church.
If you were to study both languages, you should start from Greek, because it is more difficult and you should not miss it in case you were bored by the technical nature of the Latin language. If you are going to study either Greek or Latin, think about your needs, and, in my opinion, if you'd like to help your thinking grow and deepen as much as possible, you should learn Greek.
I agree with George on all counts. The language you study first will depend on what you want it for. I think though that the Latin writers will have been reacting to their Greek predicessors and it is to the Greeks that we, and they owe the Hellenising of the western and middle eastern world. As a result the Christian religion comes out of a Hellenized society, first of Judeans and secondly of Greeks, and the Gospels and Epistles were written in Greek. Thus, I would start with the Greek language if I had it to do all over again, and I would start with Homer, and then to Attic and Biblical Greek. After this I would study Latin.