Does anyone know the specific kind of paper the professionals use for the gaming covers/booklets? The shiny kind of paper? I'd like to print out some covers of my own.

I've never made one, but from my experience in the print industry, demi-gloss 80 weight. You'll probably want to go to a printer to get a large volume, but if it's for a home project and only like one or two, you could get some thin photo-paper that is about right.

Remember though that to get the best out of your print, you'll want your printer color driver up to date and the file to print in CMYK instead of RGB.

Hope this helps!

EDIT: You could go to a printer anyway and ask to take a look at some paper samples to give you a better idea of what you want. Most places are happy to help.

Thanks!