Black and white are good neutral colors that look awesome - I had a kitchen that had white cabinets with red door fronts, red curtains and black kitchen chairs. My decor pieces where red, white and black. It really does work very well together. I'm just not sure if the color you have with a hue of pink. Get small swatches of material in the colors you are thinking of and overlay them on what you are trying to accent
Yellowish-tan goes well with red, although it is a light color that may show stains if you have pets or children.
My fiance's moms house has similar colors and her couch is gray, but a neutral color of any kind would look good.