What a lovely idea!
I don't know why, but on my hands, if I am wearing only one ring on each hand, I prefer one on a ring finger and one on another finger, usually middle but that is just because of the fits of my various rings.
I think mixing metals is so common these days and people don't really think there is anything wrong with it. An easy way to bring it all together is to wear a two-toned watch, of course. As Katie mentioned, having more than one color in the ring itself could help, too. I have a special ring I got made a couple years ago that is an amethyst I had bought for myself, the platinum wedding band of my great aunt, and a yellow gold setting my parents paid for for my birthday. All the colors look really great together and I never think about what else I wear with it. If you have a band you really like, this could lower the cost of getting a ring designed, too.