Hi jaseone, and welcome to TPF! I've moved your thread from the Articles of Interest forum over to here, where you should get better views and hopefully some answers about card paper.
Are you talking about taking a photo and having it printed on a card stock-like paper to make note cards or printing photos on photo paper (like a lot of chains do for holiday cards)?
If you are a consumer I recommend Mpix for cards. They do the photo paper cards and paper cards (Press printing). If you are a professional and want to offer cards I would get an account with Millers (mpix's big brother). They offer all kinds of card solutions and free overnight shipping. Other pro companies that offer them are WHCC, Bay Photo, etc...
If you are printing them yourself on an inkjet I like the Epson line of papers. They have photo paper and art paper. But really I have put all kinds of paper through my inkjet over the years including watercolor paper from the art supply store just to see what would happen.
Are you talking about taking a photo and having it printed on a card stock-like paper to make note cards or printing photos on photo paper (like a lot of chains do for holiday cards)?