Use a neutral colour for the cards themselves, then add colour through printing, embellishments or ribbons, or use coloured card and make a great statement. Card textures can make a big difference to the overall feel of an invitation, from rustic matte textures to contemporary pearlescent effects to vintage tapestry styles. Consider printing or foil stamping the front of the cards, or use peel_off stickers (with a steady hand!).
Then order lots of samples, as you might totally change your mind when you see them, or suddenly be inspired by the best bits of different samples. The Wedding Crafter's 'Design your own wedding invitations kit' is a pack designed to give beginners chance to have a play with different card shapes, inserts, ribbons and embellishments that can be tailored to suit any wedding colour scheme.