The gauge on that sweater, knitting on those huge needles, is 2 stitches to the inch. That's ginormous. You could easily find a cotton yarn that's worsted weight, and follow the directions just as they're written.
But to convert it to a lighter weight, i.e. a thinner yarn, you'll have trouble making that gauge. Which means you'll have to adjust the pattern and do math and all that good stuff so that you end up with the same dimensions, but more stitches. If you're up for that, I think your best bet is to start out with a yarn you really like that's light and summery (maybe a ribbon yarn? one that knits up at a large gauge?), buy it and the appropriately sized needles, and knit up a swatch to see what the gauge is. Then post again on craftster with the gauge of the yarn you bought to have someone help out with the math to adjust the pattern-- i'd be happy to help, and I know others would too. Easy.