I suggest you keep a small amount of money (~$20) at a bitcoin address, and then set the ring's public code to that address, and the ring's private code to the private key of that address.
To have someone pay you, they just scan your fist.
To pay someone you need to reveal your private key. This is less secure as once you have revealed your (unchangeable) private code to a payment terminal or another person, they can take all your wallet contents, and any money you add to that address in the future.
I recommend doing something like the electric NFC cards you get in stations. Show your private code to a scanner from a brand that you trust, and it takes the correct payment. Just be careful to only let trustworthy units scan your private code. (This is just like when you use an ATM, and you check nothing else will scan your card.)
If the ring could "sign" transactions, that would be much more secure, but you need a bit of (powered) hardware for that. (I can can help if you want to go that route too)