Helene,
Whether you do International or American is really personal preference. I started with American and am now doing International. I like them both, to be honest. What my teacher told me is that it is easier to go from International to American than vice-versa. I also think when you compete in American, the rules are little "fuzzy" and open to interpretation a little more (as Jonathan somewhat alluded to in his post above; I don't think the judges make a big stink on how bent, or unbent, your leg is when you land on it in American style). The upside of doing American is that it is more often available in social situations than International (at least in my neck of the woods).
Keep in mind, too, that International Latin = cha cha, rumba, samba, paso doble and jive. American = cha cha, rumba, bolero, swing and mambo. Maybe there are some you like better than others?!