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!).
Letterpress: The designer and paper lover's dream, letterpress is visually lovely and highly coveted all over Pinterest. However, it is expensive because it is a fine art that requires some heavy machinery. Letterpress is the option to use when you want to support the artists making it, not because you think you should. Thomas Printers is a great option for people looking for letterpress invites on a reasonable budget. The other option to letterpress is to build your own, but you better have a serious love for the actual craft. The majority of your guests, sadly, won't know or won't care that your invites are letterpressed.