Hello
For device compatibility, please have a look there : ✏ FP2 : USB device compatibility
About NFC readers, for now only SCL3711 was tested, and sadly not reported working. Though it’s compatible with libnfc on Linux, so it might be possible for a developper to add support for it.
If you have any other NFC reader, please test it and contribute your results here.
For your key : "The YubiKey NEO has both contact (USB) and contactless (NFC, MIFARE)"
Did you try it straight over USB ?
Mifare is also definitely an option, as a contacless reader is reported working on the above wiki.