In theory, the Public key could be used as a receiving address. Nice easy and not a problem.

The private key SHOULD be used as a signature to enable a payment which would be processed (and checked) on your phone/tablet.
This would be the most secure way currently we could use the NFC ring.

Any wise person encrypts their wallet which needs to be unlocked to authorise a payment.... all the NFC would do is apply this.
I personally would advise a stupidly long randomly generated password because it wouldn't need to be remembered as it's on the ring.

Think of it as the pin on your debit card. The pin machine displays the correct amount and you authorise it with your pin number.
It's a pretty okay(ish) system and all we would do is replicate that system with a much more secure pin number (4 digits vs. a very long random alphanumeric password)

I'm a bitcoiner and was going to use my NFC (private) as a cold storage wallet, so security is paramount.

And offtopic, there are already pubs that take cryptocurrency as payment. The Blue Anchor in Oxford takes Feathercoin (the feathercoin developers are from Oxford).
I was talking to them about it as I've been given the go ahead for accepting cryptocurrencies in the Student Shop I'm currently setting up (I'm a mature student studying architecture in Oxford).

I was looking at using my NFC ring (public) for payments in the shop (looking at using a Nexus 7 for the payment system).
If the students have NFC rings/devices then it's certainly easier from my point of view...