With a credit card your maximum liability for fraudulent charges is $50 even if you don't timely report a stolen card or suspect transaction; $0 if you do. For debit cards, it's unlimited.
So, for example, somebody could fraudulently use your debit card number to buy a stick of gum, hoping the charge goes unnoticed. Then, 60 days later, they drain your entire bank account, and possibly other linked accounts if you have automatic overdraft protection. If you failed to notify the bank for the gum purchase, your entire life savings is lost. Even if the bank account is only used for small purchases and only maintains a small balance, it can still create huge headaches.
Debit cards are for ATMs, and preferably ATMs inside bank buildings. Credit cards are for transactions everywhere else.
For similar reasons, you should be careful who you write checks to--because similar rules that govern debit card transactions also govern ACH transactions. And if you can help it, don't link a checking account on which you draw checks and make other payments to any of your other accounts; or at least, don't then enable automatic overdraft protection.
Most gas pumps authorize $100. Use a credit card.