I always send a money order for our down payment and have never had a problem.I can't send a cheque because it wouldn't clear thru a US bank.You can always call later to make sure that they received it.
Yes - once I make our reservations, I start to squirrel away money, and when I have a few hundred, I buy a money order and mail it off. This way, I chip away at the total, and when it's time to charge the balance, DH doesn't keel over.
We paid off the balance of our last trip, about a week or so before our arrival date, using a money order. We had saved up for the trip, so we wanted it paid off before we got there. They received it and processed it rather quickly.