Garter stitch is what you get when you knit every row.
When you knit one row and then purl the next row, you get stockinette stitch
http://knitting.about.com/od/stitchglossary/g/stockinettest.htm
HOWEVER, when you try to knit a scarf in stockinette stitch, the edges have a tendency to curl in. What most folks tend to do is knit a border in garter stitch: knit the first few rows, and then instead of purling all the way across on the purl rows, you knit the first five (or however wide you want the border to be) stitches, purl across until there are 5 stitches remaining, and then knit those last 5.
Seed stitch (K 1 stitch, P 1 stitch) is also a good border but explaining the difference so you get the seed pattern instead of K1P1 ribbing is kind of tricky.
http://knitting.about.com/od/stitchglossary/g/seedstitch.htm