At the moment, I'm playing with Kumihimo. Joe bought me a disk kit, which included the disk, 8 bobbins, and instructions for 8- and 16-strand versions of an unnamed braid that turned out to be kongoh gumi Z.
My disk is the BeadSmith one, I hear the Hamanaka (designed by Makiko Tada) is also good. These are made with dense, thick, durable foam and are large enough to manipulate easily. I hear other brands & materials either disintegrate (the foam is less dense, or too thin), or don't hold onto the strands well.
Thick foam means you don't need to weight the strands. I used a weight on the band at first, but I'm not finding it important (yet), and it tangled with the threads.
I used the bobbins at first, but found them fussy. For test pieces I find it easier to work with threads of 1 yard or less, and just untangle them manually. When adding beads to these short pieces, I prefer putting on only as many as will fit on the face of the disk, so the bead thread doesn't tangle with the other threads.
I used it to distract my hands while watching the Olympics, and now that those are over, I find it is still in my hands most evenings. I am enjoying the tactililty, and the minimal equipment and knowledge required to start. I am particularly enjoying the more mindless structures, which allow me to watch TV or movies and braid without missing too much.
At first I tried to figure out what book to buy. After looking at the ones I could find at the library & weaving store, I realized that most either don't cover using the disk (they are for the marudai), or they only cover a couple of structures. So I searched online, and found a lot of info. It sounds like Makiko Tada's book 6 in her series on structures (the one for disk & plate) might appeal to me, but I haven't seen it yet.
Speaking of Makiko Tada, you really must check out the video on her blog, of an industrial braiding machine she designed. Dreamy! The photos of braids there are really exciting, too.
Free Resources Online - a short list
Weir's Dolls & Crafts has free instructions for Kongo Gumi, Reversed Kongo Gumi (so you can make zigzag patterns, etc.), a ridged spiral Kongo, and Edo Yatsu on the disk, and Anda Gumi, a ZigZag braid, and Une Gumi on the plate. She also covers adding beads (in the project instructions for the beaded leaf and ladybug necklaces), and finishing ends. This is more info than in many books! She sells equipment too.
Craft Design Online's kumihimo page has tools for designing several braid structures (so you can see how your colors will come out). Each structure's page also includes instructions for making that braid, although the instructions are written for the marudai, so you'll have to adapt it to a disk.
The Kumihimo Companion is a database of detailed information the author has compiled about what structures are contained in each of numerous books, links to suppliers and information, a way to cross-reference within the database so you can see which books cover a certain structure, and more.