I wouldn't recommend paying with your debit card (linked to your bank account). Hotels often place a "hold" on a certain dollar amount in your account with debit cards, "freezing" that amount from the time of check-in. They can place a hold on the amount they think you'll be spending, which can be a much higher amount than you plan to actually charge to your room.
Because this amount is held (basically "Frozen") from the day you check in (rather than when you actually check out), it can really goof up your available funds in your bank account. If you have automatic payments set up on certain dates, you might not have the funds available, and you end up with NSF (non-sufficient fiunds) fees.
I work at a credit union, and feel so sorry for our members who come in because they've been charged NSF fees, all because some merchant or hotel has placed an unexpectedly large hold on the funds in their account. Most peple don't realize these merchants are allowed to do this. Even if you spend $30 at a gas station, the merchant can place a hold on a much higher amount until the charge is posted!
So my advice is to charge to your room but pay by credit card. That's what gives you the most protection. You can pay your balance in full when you get your credit card bill. (I myself don't use Disney gift cards, for the simple reason that if you have to cancel your trip due to an emergency, all of your money -- potentially hundreds or thousands of dollars - is tied up in cards you can only use at Disney!)