We put anything and everything on our credit cards, gas, groceries, doctor visits, utility bills....everything. We pay the balances off every month; therefore we never pay interest, never. And the rewards we earn are significant. We love our credit cards.
I always use my credit card when shopping online, credit cards have built in identity theft protection that debit cards don't. I don't worry about my transactions with Eden being an issue, but I always use my credit cards when shopping online.