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/Sparrow78/x-nature-shawl
(I’m not familiar with the yarn she used, by the way.)