For straight knitting, you can use circulars or straights. For knitting in the round, you can only use circulars. Also, with circulars, the weight of the fabric you create as you knit is distributed more evenly over the cable, so it is much easier on your hands and wrists. Finally, with circulars, there are varying cable lengths so the number of stitches that you can have on the needle will vary widely. You can only fit so many stitches on the needles.
You can use your learn to knit DVD with circular needles because the technique is the same as with straight needles.
Having said all that, your DVD will probably have you starting off with small pieces of knitting, so I'd recommend getting a short circular (16") to start out with, because you might find one with a longer cable "fiddly" to work with for a smaller piece. But I think you should start off with the circs!