The pattern states that you will require 4.5mm and 5mm needles in both straights and circulars. However, the entire pattern can be done on straights, especially the smaller sizes. I think the circulars are used for when you have too many stitches to comfortably hold them on straights, they are never used for actually knitting in the round.
I think this is an important FYI, since I actually went and bought 5mm circulars and then never needed them. In fact, the only reason I used my 4.5mm circulars was because I did the finishing in a different order then the pattern states. I worked the cuffs, then seamed, then I picked up stitches for the border on the circular. The instructions actually have you work the border on the back and the fronts separately, and then seam.