I've had good luck with USAA. The only time I've called them and told them I'm traveling was when I went to Asia. I only fly Domestic, Caribbean, and Mexico. But never call and never had an issue.
I have been told that if you can you should use your credit card over bank card. You have many more protections with credit if your info is stolen. If your checking account is drained via your bank card info being stolen it can be much more difficult getting your money back.