Stockinette stitch is knit a row alternating with a purl row if you're knitting flat, or knitting all rounds in the round. You need to cast on more stitches to get an accurate measurement and don't measure on the edges as those stitches will be different than in the middle. So CO about 36 or 38 stitches and work for about 10cm in lenght. Ideally, the gauge swatch should be washed the way you will the finished item. I don't know about the circular needle, it may be used to hole a larger number of stitches. If you can link to the pattern or say which one it is, we can help you a lot better.
sue- knitting heretic