Credit vs. Debit has nothing to do with being debt free. If you are worrying about not keeping track of what you put on the card and putting too much on the card, just call the card company and ask for a low limit.
This is just my opinion but if you are worrying that you aren't keeping track of spending Debit is the WRONG way to go. Say you set aside $600 that you are willing to spend on the vacation. When you receive the credit card call and ask them to reduce the limit to $600-$650. If you find yourself in an emergency situation (car repair, medical, or overspent and stranded) you can call the Credit card company and ask for an increase to the limit. You can go home safely, you have $600 in the bank to pay for the budgeted items and 1-1.5 months to pay for the emergency items interest free.
If something happens when you are using a debit card or cash you are simply stranded, with no contingency plan.
There are tons of no fee credit cards around, but finding a no fee debit card is next to impossible in my area. This means every time you use your debit card it costs $0.05-$0.20. Credit card companies always review for unusual purchases but debit cards seldom do. And again credit cards generally have better fraud and theft protection, so you'll never be stranded with a credit card, but having your debit card stollen could leave you stranded, and out of pocket for ALL fraudulent charges.