Most good credit card companies will hold you accountable for only $50, if anything, when somebody steals your card or info and goes on a spree. If they don't, I wouldn't get a card with them. We are not responsible for anything we did not purchase, and just recently had some random charge, which we disputed, and did not have to pay (we have a CapitalOne card).
Definitely use a credit card whenever you shop over the phone, online, etc. *Most* (not all) banks have zero protection, meaning if someone gets your debit card info and cleans out your account, you're out of luck and money.