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!).
As a graphic designer and someone who pulled out all the stops designing her own wedding invitations, believe me when I say you can make DIY wedding invitations as simple or as complicated as you want. A lot of people go into making their own invitations hoping to save money, but I'll tell you up front: there are plenty of affordable places to get nice invites with less work than it will take you to DIY wedding invitations. However, if you have specific reasons to go DIY on your paper (like, you want to bring your specific idea to life, or you want to get creative) read on. (Fun fact: Every APW editor DIYed their wedding invitations, so we've got your back here.)