For my ink swab catalog, I use Bristol Artist Trading Cards. They come in a variety of finishes, but I personally prefer the Smooth version.
To put the swab down, I use a long-handled cotton swab. I have found that technique is vital in order to get a consistent behavior when swabbing inks. For starters, I dunk the cotton swab several times. I have found it's not good enough to just let it sit in the ink. The action of dipping it several times does a better job of getting the swab thoroughly saturated. Then I start in the upper left hand corner of the card and swab down to the lower right. This gives me a sense of the range of colors available from the ink from super wet to mostly dry. It also allows for pooling to highlight any sheen the ink may have (although the artist trading cards aren't the best paper for highlighting sheen.)
I hand write the name of the ink under the swab, manufacturer first. I generally prefer to use a filled pen for this rather than a dip pen, as it gives me a more accurate indication of what the ink will look like in a pen. (I generally try to swab inks when I ink them rather than doing them in big batches.) If I am doing a big batch, though, I will use a glass dip pen that I wipe off, dip in clean water to thoroughly rinse off, then wipe dry on a separate cloth to prevent cross-contamination.
I stored my inked cards in any business card holder I can find. Artist trading cards aren't exactly business card-sized (they're a little larger) so I tend to find business card files without a lid.
I also like to photograph and color correct each of my swab cards. I use Adobe Lightroom to organize and tag my photos. I tag them by manufacturer and by color family, so I can do quick comparisons of inks digitally as well as in person.