Earlier today, Apple posted two support documents detailing frequently asked questions about Apple Pay and the security and privacy of the service.

From the FAQ:

When I’m paying in a store using my debit card in Apple Pay, should I choose Credit or Debit on the terminal?

When presented with this choice, we recommend you to choose “Credit” to get the most consistent Apple Pay experience. Choosing “Debit” may not always work successfully with some older merchant payment terminals and backend systems.

And about security:

When you pay using Apple Pay in stores

Paying in stores that accept contactless payments with Apple Pay uses Near Field Communication (NFC) technology between your device and the payment terminal. NFC is an industry-standard contactless technology designed to work only across short distances. If your iPhone 6 is on and it detects an NFC field, it will present you with your default credit or debit card. To send your payment information, you must authenticate using Touch ID or your passcode. No payment information is sent without your authentication.

MacRumors has a list of the retail stores that have begun accepting Apple Pay in the US today. Apple has also launched an Apple Pay section (currently on the front page of the US iPhone App Store) showcasing iOS apps that have been updated with Apple Pay support, including the Apple Store app.