It surprises me all the time to see what you can do with a CC in America. Here in Europe it's also very common to have a direct debit card. You don't have a monthly bill, but the amount you spend is directly deducted from your account. Lots of people prefer that.
The best option in the US is to use a credit card as if it were a debit card, and pay your balance off every month. This way, you get to take advantage of the better fraud protections, cash-back rewards, and balance-smoothing benefits of the credit card, without paying any intetest. And it improves your credit score.
Unless you have no financial discipline, there's no reason to use debit over credit.
As coming from a country where debit cards are widespread (France), and living in one where they barely existed until recently (Japan), and having had my (japanese) debit card fraudulently used (still a mystery how ; not stolen, barely even used at all ; last use 8 months prior), I now know that credit cards are better in that case: if you notice the fraudulent use early enough, it's not going to hit your account, while I'm now stuck waiting for a reimbursment that will hopefully happen 3 months after reporting the event.
Just for that, I now prefer a CC, not using the "Credit" part of it. Edit: well, technically, I'm using it, but only as a buffer.
But it's always awkward to be asked "single payment?" for ridiculous amounts like $20. Huh, yeah, why? are people really paying such amounts in multiple installments?
I just use my credit card as a debit card. In the US, consumers have better financial protections against fraudulent charges with credit cards than debit cards.