Personally, I feel it's best to get a running start on one language and then start the other. At least get the basics of one language down so you can kind of "relax" with it more while you get up to speed on the other. But you certainly shouldn't feel that you have to master one before starting the other, since that may take years.
As to which one to start with, it may not matter that much, but it kind of also depends on your background. If you haven't studied any other languages from a grammar-intense standpoint, Latin may be better to start with. I think beginning Latin is a little more straightforward than beginning Greek (just an opinion, others might disagree!). On the other hand, I've personally found that once the basics are mastered, it's easier to advance in Greek than it is in Latin... Greek just seems more intuitive to me than Latin. I don't know why.
There are no hard and fast rules, but that's my input. Hope it helps.