If you're buying your own paper, you can find a good selection at local office shops when it comes to card stocks and glossy photo paper. However, if you're looking for linens or specialty papers, you may have to go online. Always get a sample before buying a huge stack of paper, and do a test print, to make sure that whoever or where ever you're printing from can actually use the paper you've selected with your design and medium. Here are a few other places to buy paper from.
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!).