ONLINE PRINTING: There's a pretty wide variety when it comes printing via online companies, so always make sure you can get a proof of your invitation. With some companies, that may cost extra, but it's usually not very much. Much like with at_home printing, your paper options will usually be limited to whatever the company carries, and each company's paper set is going to be slightly different. You can usually request paper samples for free. Here are a few companies I've used with good results:
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.