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.
As a graphic designer and someone who pulled out all the stops designing her own wedding invitations, believe me when I say you can make DIY wedding invitations as simple or as complicated as you want. A lot of people go into making their own invitations hoping to save money, but I'll tell you up front: there are plenty of affordable places to get nice invites with less work than it will take you to DIY wedding invitations. However, if you have specific reasons to go DIY on your paper (like, you want to bring your specific idea to life, or you want to get creative) read on. (Fun fact: Every APW editor DIYed their wedding invitations, so we've got your back here.)