Both your debit and credit card are covered by protection from Mastercard and Visa. Therefore, you have backup for transactions that are disputed or fraudulent on both types of cards.
Your card issuer should be able to provide toll free numbers that you can call for assistance when traveling, if you ask them. Makes it easier, if you have a problem.
You should have card numbers, CVV codes (on the back), and phone numbers of issuers for all cards in a secure place. How you deal with the "secure place" is your call.
Different issuers charge differently for foreign transactions. Cap One does not charge that fee, so it is a good deal. But it will charge a higher rate for cash advances, so it is only good for purchases. A lot of credit unions charge a lower rate on debit and credit cards (mine only changres 1%) so do your research, because using cards overseas will cost you something. Besides the foreign use fees, there are also ATM use fees charged by both the card issuer and the financial institution you are using. So, taking out as much as possible at a time is the way to go.
You should ask to have your debit card ATM levels as high as possible. However, some ATMs limit tthe amount you can withdraw. SO both will impact your amounts of withdrawal.
OK, so I have worked in banking for many years. Does it show? Hope this information is helpful!