Stockinette is going to curl because of the way the yarn is wrapped around the sts. You need to have a border around it, so you would knit about 4-6 rows, knit the next row and on the purl row knit the first and last 5 sts to keep it them in garter stitch. This frames the stockinette and helps keep it flatter.
If you're using a backward loop cast on, that's not a good one to start a project with, it's loose and loopy. Try the knit or cable cast on shown in videos on the cast ons page.
sue- knitting heretic