Great job on your clearance plant! There are thousands of cultivars of the plant commonly sold as Christmas cactus. You can see some of them in the general entry on here:
Christmas Cactus (Schlumbergera truncata)
And/or look at the individual, named cultivars:
http://garden.org/plants/searc...
As a succulent, it's best to let cuttings callous (dry/heal) at least overnight before putting in water or soil. There's a huge contingent of believers in both methods. A google image search of "Christmas cactus propagation" should visually inspire you, and show lots of options.
