One of my prayer shawl patterns is very simple. One row is K1 P1 K1 P1. The other row is Knit all stitches. That's it. Just repeat those 2 rows.
You can use any size needles -- I use large needles and worsted weight yarn. If you are concerned about washing it and want it to be more tightly knit, you could use smaller needles, like maybe 6, 7 or 8.
Sometimes I do a garter stitch at both ends of the shawl, as well as the first and last 4 stitches.
Hope this helps.