AT_HOME PRINTING: By far the most accessible, this is easiest option for tackling the project in smaller chunks on weeknights rather than spending hours in a studio or waiting at a print shop. However, you should test paper before buying a ton of it, printers can be especially finicky, and your can't exactly change the ink your printer uses. If your printer isn't higher end, you may have very limited paper options. Here's a little more on at_home printing.
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.