Finish: Your paper finish will affect how you're able to print and how much ink your invitation will take. Glossy papers take a lot more ink and longer to dry. Linen papers and papers with more texture have a much higher tendency to bleed, and so they won't work with some at_home printers where you can't change your ink settings. If you're not interested in researching finishes because you're not a weird nerd (like myself) who likes to feel on paper, a matte card stock is an easy, relatively foolproof option that will more than likely work for the printer you're using.
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!).