My guess is that any color but red will work. But just so you're not regretting it, use a rinse that only lasts a short while - long enough to get used to it, but not so long you have to wait for it to grow out. If you like, then you can go for something that lasts. Or, maybe someone you know has a program that lets you take your photo (looking straight ahead) and try different hair styles and colors. I don't have a name but I know they make them.
The best thing to do would be to dye your hair the color of your roots or a little lighter. I wouldn't go too dark if you've never had dark hair before (i dye my hair all the time and a wicked color change can be really too drastic sometimes).
But I think all blondes can pull off being brunette, just not too dark.