Weight: Paper thickness is measured by weight. The higher number you see, in pounds, on the packaging label, the thicker your paper is. This doesn't mean you have to find the thickest paper you can—most card stocks are a great weight for invitations and can hold up to being mailed.
Letterpress: The designer and paper lover's dream, letterpress is visually lovely and highly coveted all over Pinterest. However, it is expensive because it is a fine art that requires some heavy machinery. Letterpress is the option to use when you want to support the artists making it, not because you think you should. Thomas Printers is a great option for people looking for letterpress invites on a reasonable budget. The other option to letterpress is to build your own, but you better have a serious love for the actual craft. The majority of your guests, sadly, won't know or won't care that your invites are letterpressed.