Card machines in the US have confusing incorrect terminology. Debit Card does not mean debit card, and Credit Card does not mean credit card. Debit Card means “uses one of several local US inter-bank payment networks”. Credit Card means “uses the Visa/Mastercard/JCB/etc payment networks”. Whether your card is a debit card or credit card is of no consequence. Unless you have a card that can use a local US inter-bank payment network (which no UK-issued card can AFAIK), you need to select Credit Card whenever asked.
Some people have had issues in the past with the NY metro machine requiring a postcode. The advice seems to be:
Edit: See the Card Usage section of the USA wiki for more details on the debit card/credit card issue in the US, there are some intricacies I didn’t capture above. 