Besides variances on which ring comes first, there's also the religious aspect which dictates which HAND the rings should be on--left vs. right.
Wedding ring - Wikipedia, the free encyclopedia
I went along with this one: "Another practice holds that the woman should wear the wedding ring above the engagement ring, thus sealing the atmosphere of the engagement into the marriage."
But it wasn't really the sentiment of it all that made me choose to wear my engagement ring under. It was because after having been with the guy for hmm, 11 years, he thought his wife-to-be had chubby fingers (Size 6 loose even on my thumb...) when he went to pick it out. I'm not the kind to care enough to get it resized.
It was hilarious how it just kept flying off my finger for the entire time before I had my wedding band (Size 4.5 and still slides off fine) placed on top of it to hold it in. LOL. He's lucky I'm not a jewellery kind of gal to begin with.