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.)
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.