I would always use the Paypal option online if available instead of the merchant's cc processor, no cc number shared.
And this is just me, but I NEVER use my bank account debit card for online purchases. I try to stick to one credit card for use with online purchases, one with a lower limit and rock solid fraud protection.
All the above applies ten fold for international online purchases, and I would say probably 100 fold for online illegal rep trade.