Do you know about the the Fair Credit Billing Act? Because of it, the federal limit of liability on a single credit card is $50. If you report the card missing or stolen before it's used, your liability is $0.
For this reason, many consumer advocates recommend using credit cards for online purchases. Not because the card is safe (it isn't), but because of the low liability for unauthorized purchases. Debit cards, on the other hand, can be used like credit cards, but do not have the same protections. Also, as a direct line to your checking account, unauthorized purchases could suddenly empty your account.
Note that the liability limit is $50 per card, not per purchase which is even better protection for you. There is also no time limit specified on the FDIC's website (which doesn't necessarily mean there isn't one, but it looks promising so far).
I still recommend avoiding sites that force you to make an account and store a credit card for service (for example Amazon.com), but you are far better off for now using a credit card than debit no matter where you shop.
There are often limits of liabilities for debit cards as well, but those are voluntarily enacted by your bank. Check your specific agreement details first.