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.
Then order lots of samples, as you might totally change your mind when you see them, or suddenly be inspired by the best bits of different samples. The Wedding Crafter's 'Design your own wedding invitations kit' is a pack designed to give beginners chance to have a play with different card shapes, inserts, ribbons and embellishments that can be tailored to suit any wedding colour scheme.