For this reason I usually use a debit card as you can check more frequently what is going out of your account.
I have a credit card with my bank, and can check it through my online banking, just as I can the debit card.
I have a specific credit card to use for online and phone purchases, with a credit limit I keep low, but use my debit card when out and about.
However, now that vendors have mobile apps to take your credit or debit card, I think I shall have to start using the credit card in those situations too. (Just been at Woolfest and didn't like the idea of my debit card details being taken by who knows what mobile devices and apps. Will get a PIN for the credit card and use that next time.)