The devil's in stopping Persia, you're right. If you are Greece, it makes the strategy relatively straightforward - take out Persia, and forget about Rome when you can. Otherwise, I find it important to put some thought into not fighting Persia's enemies when it might help Persia. If you're Rome, you might want to build a bigger empire faster than Persia... but perhaps without fighting Greece and thereby helping Persia. If you're Carthage, you may want to go east to fight Persia, or at least help Egypt if they are being invaded. If you're the Teutons, you're pretty much out of luck.
But there probably are some good stories here with more specific, and likely more successful, strategies.