Problems with color in art prints
It's disappointing to spend time on a painting that turns out well but reproduces poorly. To get the best colors in prints, create your painting with colors similar to those used in printers' inks: magenta, yellow and cyan. In recent years manufacturers have offered artists good matches for these colors in pigments. Quinacridone Magenta is a close match, but you can also try Permanent Rose or any other bluish-red. Any yellow that isn't too orange or too green will work, such as Transparent Yellow or Hansa Yellow Light. The best cyan I've found is Winsor Blue Green Shade, which is about the same as Thalo Blue. You need a greenish-blue. Using a limited palette of "safe" colors will assure that your print will match your painting.
Even if you don't plan to print, it's wise to use a somewhat limited palette; you don't have to worry about the color gamut. Here's more on limited palettes and using triads in painting.