Hi there--
I too am a new dance student, and like the other posts mention dancevision.com is really good. Depending on what type of ballroom dancing you want to learn, I really recommend the DVDs with Ron Montez and his wife Carla. The dialogue and instruction are really clear, precise, and they don't rush through anything. They illustrate the steps slowly and go over everything with detail so it's easy to follow.
I bought the west coast swing DVD w/ Ron Montez and it rocks. I also got the Rumba DVD with Corky Ballas; his videos are also equally good. For Cha Cha I bought Karina Smirnoff and Slavik's DVD, and I love it, although I think this is more for slightly advanced or not pure beginners.
One DVD that I DON'T recommend is the Salsa DVD w/ Jose DeCamps and Jami Josephson. Jami herself is great, she speaks well and is a great instructor, but Jose is retarded and listening to him speak and try to narrate throughout the video is one of the most painful experiences ever. I got so frustrated and annoyed I stopped the DVD and use it as a coaster now.
Hope this was a little helpful.