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.