A word of warning about debit cards....
If your debit card number is compromised and someone makes large purchases, your bank is unlikely to indemnify you. They are not required by law to do so. You will need to pay off whatever is overdrawn on your account before you can initiate a dispute as to whether or not the bogus charges were fraudulent.
On the other hand, if your credit card number is compromised, you can claim fraud immediately and not be required to pay for the bogus purchases. You are, however, required to cooperate with any investigation into the fraud. I recently had someone take several THOUSANDS of cash against my credit card in Kenya. After signing my notorized signature on a fraud affidavit, those charges were removed and I am not responsible for them.
My husband never carried cash and always used a debit card until I met him. I advised him of this potential problem with debit cards, so he agreed to become a joint user on one of my credit cards (we were living together but not married at the time). He actually did this to humor me, thinking that I was giving him inaccurate advice. However, he subsequently got a job as a software developer at a bankruptcy law firm and the attorney there confirmed everything that I said was 100% accurate.
Another thing to think about...
Edit: you can always get a prepaid credit card so you don't overspend, but they can charge some pretty insane account maintenance fees.