Personally, I would always register a credit card with online services rather than a debit card. For a start, this will avoid any surprise debits from your bank account which could lead to you going overdrawn. Secondly, you always have greater protection with credit cards under the Consumer Credit Act (although you can always raise disputes relating to debit cards under chargeback rules, but this is just a little bit more complicated and not enshrined in law). Also, if you had a charge on your credit card, you would have time to resolve it, and you can always refuse to pay off the element in dispute if necessary.
Another tip I've known people to follow is to use a separate card for all online purchase to those made in the real world. Thus if one gets compromised, you still have another you can use whilst you get that one sorted out.
Personally, I've been a victim of credit card fraud twice, despite having worked in the industry and knowing what to look out for and the precautions to take, In both cases, I was still in possession of the card in question.