I love copper and bronze rings. I like the deep warm colours, but on some people these metals can turn your finger green underneath the ring.
Each person's skin reacts to copper in different ways. Maybe it has something to do with moisture on the skin, I'm not sure, but the effect is harmless.
For most people a pure copper ring will turn your skin green when worn but for some it doesn't. Only way to tell if it will happen to you is to wear a copper ring as a test. If your skin does have a reaction to the copper the green mark will usually disappear overnight (if the ring is removed) or will easily wash away with soap and water.
This is less likely to happen with bronze rings as the copper content is much smaller. My own fingers get green from pure copper, but nothing happens with bronze or indeed sterling which has 5-7% copper.
If you want to try to prevent the ring from turning your finger green you can apply clear nail polish to the inside of the ring. The nail polish coating will prevent the ring's metal alloys from coming in contact with your skin and prevent your finger from turning green. The clear polish will eventually wear off and when it does just add another application of the nail polish.
Usually bronze rings also get a bit of a patina on the inside with wear and this seems to stop the reaction too.
If you hate the idea of your finger turning green, then go for a silver ring instead. Especially if you work with water a lot as the extra moisture seems to accelerate the effect.