Welcome to ballroom dancing!

No, it would not be difficult to learn international later if you learn american style now. Most social dancers do american style, unless you're at a studio or an area where primarily international is taught (where I live, very little international is done at social dances). The technique for smooth and standard are the same, it's just the choreography that's different. The technique is a little different between latin and rhythm, but rhythm is slowly evolving to look more like rhythm! I've done a lot of both american and international, and I like smooth better than standard but am about even on latin and rhythm...so, that probably doesn't help you, but gives you something to chew on, I guess! :)

As for the contract, it depends...don't automatically assume you're being taken if they ask you to sign a contract, but you do want to be careful. At some studios (chain and independant), they try to get you to buy 20, 50, even 100 lessons at a time. At my studio, we have you sign a contract promising to buy 5 (yes, five) private lessons to get the "bulk" rate of $40/hour...if you don't do a contract, you pay $65. For group classes, you can pay as you go or buy a punchcard to get a lower rate. That's just how my studio works...and every one is different! You just have to shop around.

Good luck and have fun!