I strongly advise against using a debit card online ever. If anyone ever hacks your $site_of_choice and gets your debit card, you can be responsible for everything the hacker uses that card to purchase. With credit cards, you are limited to (I believe) no more than $50 USD no matter how many hundreds of thousands a hacker rings up.

An alternate suggestion would be--I think AmEx does a special type of card where you can't use it anymore until you pay it off in full. It might be possible to get one of those, cut up the existing ones (keep the account open but never use the card, if you're concerned about your credit rating), and go that way.