What shade of brown are you naturally?
I'm like you. I have green eyes (mid/dark) and very fair skin, but I've been blonde all my life, I'm getting really sick of it, and I'm really hoping to go darker sometime this week. (This is why your question caught my eye -- I'm also curious.)
Anyway, if you have light brown hair, I wouldn't be afraid to do darker if I were you to a mid brown (especially if you have darker eyebrows, which I, sadly, don't. (But eyebrow tint was invented for people like me.)) I think mahogany tones can look utterly striking on pale, green eyed girls, but I've browsed around sites recently and if you're very fair you should apparently avoid red tones. But everyone's different and some people can just make it WORK.
I don't think it would matter if you went lighter or darker, since there are arguments that both can make you look washed out, although I really think that's a matter of being too light or too dark. My advice: choose lighter or darker as you wish. I don't believe that people with a certain skin tone can only pull off one colour, and anyway - if you get bored of one you can try the other, as I am.
I know I probably wasn't too helpful, but good luck!