I have a friend that is a redhead, and I have seen from her experience that trying to color red hair can be a problem. The red has a tendency to show through in most dyes. (hence why there's a tiny label on boxed dyes that states that people with red hair will have redder results.) She used a temp. brown dye on her hair at one time, but the result was auburn instead of true brown. If having some red in your hair even after coloring it doesn't bother you, then have at it. It's less damaging to your hair. A permanent color in the right shade and tone would probably be your best bet if you wanted to completely eliminate the red though. If you were to choose to go the permanent route, I would recommend purchasing a shade with an ash tone. Ash tones are better at reducing the appearance of red and golden tones in hair. A few at-home dyes I can recommend are Clairol Natural Instincts (if you're going temporary), and Garnier 100% Color, Herbal Essences Color, or Clairol Hydrience if you'd want to go permanent. Good luck!