Payment is best made with a credit card. Although outright fraud is uncommon you have some chance of canceling the payment with a credit card. A check or cash is gone without a legal battle , that can be difficult, outside your home area.
Make certain you know all charges and costs up front and before you leave home.
It is best to take out travel health and flight insurance. Your flight may need to be delayed if your recovery is not fast enough. Remember that you can still get ill with other problems, unrelated to your surgery. Unless you have travel health insurance you may end up with a very large medical bill.
If you have a complication of surgery, like bleeding, you may need more than one operation and consequently more expenses.
If the price is not in the currency of your own country, check the exchange rates and know exactly what you are getting for your money.