Support for usb devices on chromeos is crap. Keyboards, mice and disks are about your lot, so don't rely on a usb card reader working at all - it would probably need dedicated windows software installing. You might be lucky if the card reader acts like a keyboard, in which case a web form could pick up the details it transmits.
NFC has nothing at all to do with reading credit cards as far as I understand it. NFC is a way you can make a prtment with an android phone instead of using a card.