I usually use USPS Priority International. You can insure the package up to $5000 that way, and it's not horribly expensive. Also, it's trackable.
Go to the USPS website, pick Priority International shipping, find what zone your destination country is, and then do your best to estimate the package size and weight. That'll get you in the ball park for shipping cost, then add some for insurance. Can't remember if the website will calc that for you.
That's my advice.