I would be slightly wary of giving a debit card, as what happens with a credit card is they put a "reserve" amount on it, say $500, not fully processing it, but a bit like a deposit to make sure you have some money. At the end when you get their bill, they cancel the hold, and charge you the proper amount. Immediate and straightforward.
If you use a debit card, they cant do that, and have to actually take the $500 fully, then process it as a refund when your final bill is known, and the the refund can take a week or so to do, plus the actual amount you are billed. Lots more room for problems.
So in my opinion (for what its worth!), either a credit card or cash is the best bet, or possibly get one of the loadable credit cards, which you buy, then add a balance to, then use like a credit card.