One of the questions I get most from customers is 'Where should I get paper?' My stock answer (yuk yuk, get it? stock, like card stock? anyway...) is that you can go to Office Depot or Staples and just grab card stock and matching envelopes. This will work fine and will be very affordable (more info about paper and weights in the e.m.papers paper guide).
However, there are some online vendors that really stand out. Here they are:
French Paper is one of America's oldest family run paper mills, and a very cool company to boot. They've got an outrageous assortment of colors and stocks, and they've always been good about getting exciting designers to create their catalog. I remember them from art school as a B2B company (business-to-business) but now they sell directly to customers online. Lucky you!
LCI Paper is a paper company that has developed their website with exactly you in mind. They've got a ton of excellent video content on how to make wedding stationery at home and an endless selection of papers, envelopes and card stock with detailed descriptions and instructions on why/how/which kind to select.
Paper Source is a well known online and brick-and-mortar retail store with all kinds of paper goods. In addition to crafting supplies and seasonal stationery, they've got a good supply of envelopes and card stock.
Cut Card Stock is a site I discovered in the comments of one of my favourite wedding blogs. They've got a wide selection of, well, cut card stock. They also sell smaller amounts in difficult to find sizes. A note: If you do buy pre-cut card stock make sure to use only designs with no bleeds (color or design that goes off the page) like this one, this one or this one.
Envelope Mall is just what it sounds like, an online store chock-full of envelopes. Not only do they have zillions of styles and colors, they also do envelope printing (100 minimum) and card stock printing.
Ordering paper online is trickier for my European customers. I can't point them to a single all-in-one online paper provider like the ones listed here. So consider yourselves lucky, North Americans!