Just tell a cool family member who understands first. My family is so anti-Greek! I can even quote my brothers for saying things like "I don't need to buy my friends" and "I don't need letters to prove my manhood." Since my big brother is a nice balance between being my friend and like a parent to me, he was the only one I told in my family that I was rushing. Yeah, he did say some things about the Greek system, but he also said "Do whatever makes you happy. Don't let Mom and Dad stop you." Once you get the support from someone who both you and your family respect, they're more likely to warm up to the idea of you being Greek than if you just walk up to them and say "I'm Greek and you can't do anything about it!"

Greek to Greek,
That1LoudChick

P.S. I'm the first and only Greek in my family, too!