Credit Card or Debit Card? Credit Card!
If you have the option, the safest way to conduct transactions from your phone or on the Internet is by using a credit card. If a problem occurs, the Fair Credit Billing Act can protect your rights. Plus, you can dispute charges on a credit card and withhold payments on those charges while the investigation is taking place. (You can’t stop paying your entire bill; just payments on the portion of your bill that is under dispute.)
Debit cards do not receive the same federal law protection as credit cards, and by the way, online checking account transactions can also expose your account to fraudulent activity.
Also consider using only one card for all mobile and online transactions. That way you can monitor your statements and activity more easily, and you don’t put multiple cards and accounts at risk.