I've used my debit both times with no problems. I really never use my credit card unless its for something big-let's say the down payment for the next cruise (I wish!). I just make sure the money is there for the trip. They will charge the card when your account hits a certain amount. I believe it was around $250.
One thing to remember is that if you have a daily limit per day (ie. $1000/day), you might want to call your bank if you want a higher limit. The reason at our bank is to make sure that if your card is stolen and used, they could not exceed that limit. We have had it happen that we were over our limit for the day. This was because even though we did not charge it all on one day, (it just happened that one day was a Sunday) all the charges from the Sun and Mon hit on the same day.