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.
ONLINE PRINTING: There's a pretty wide variety when it comes printing via online companies, so always make sure you can get a proof of your invitation. With some companies, that may cost extra, but it's usually not very much. Much like with at_home printing, your paper options will usually be limited to whatever the company carries, and each company's paper set is going to be slightly different. You can usually request paper samples for free. Here are a few companies I've used with good results: