You can dye your hair straight to brown with no golden tones to it. There are various shades of brown you can check out but this will vary depending on the tone of your skin and what you want to achieve. You can get in touch with a hair specialist for some of the best recommendations.
If you wanted a dark color then you would have to dye the part you want colored brunette first so then your hair can take the major color change easier. This prevents hair trauma and causes it not to fall out.