The recommended needle size is 8 to 10, so that's probably worsted weight yarn or somewhat smaller. If you're buying locally at a big craft store, you might look at Lion Brand Wool-Ease, I Love This Wool at Hobby Lobby, Simply Soft by Caron (acrylic), and Vanna's Choice (another acrylic).
For online purchases, check out the worsted weight yarn at Knitpicks
. I'm sure someone else will chime in and give you some other recommendations for yarns found mostly online or at specialty yarn stores.
Also, I found this pattern on Ravelry, but only one person has made it. You might look at her notes, though, and see if you get any ideas: http://www.ravelry.com/projects/Spar...x-nature-shawl
(I'm not familiar with the yarn she used, by the way.)