Reddish Face and Hair Color
A: First of all, I would avoid cool tones and those with green or drab base colors (the ash blondes and browns). The blue and green base colors would result in hair color that will only emphasize the redness of your skin.
If your natural color is a dark brown, you may see a lessening of the appearance of the redness by lightening the color a little with a neutral base color, but going to a color that is darker will almost certainly make the skin look redder by washing out the base tone and making the redness more prominent. Conversely, if you lighten your hair too much, you're going to emphasize the redness because it will be such a contrast to the lightness of the hair.
Obviously, you want to make sure that any color choice won't conflict with your hair's natural color. To do this, make sure to check for your hair's base color by stepping outside into natural sunlight and use a mirror to look at your hair in this light. The general tone of the glinting of the hair color will give you the base color for your hair. This will generally be: golden or yellow, yellow-orange, orange, red, red-orange, blue, violet, blue-violet, red-violet, drab (green) or neutral (no discernable base color detected).
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See also:
How to color hair
Cool and warm hair tones
Hair colors and our color palette
How to match hair color to your skin tone