10 foot? That is really long.
The size of needles depends
- on the yarn (thickness) you use
- on the look you want to have.
Yarns can be knit with a variety of thicknesses of needle for one yarn. Bigger needles leave more holes, smaller make a more dense fabric.
you can, of course, technically always go bigger and bigger with the needles, but at some point it becomes hard (to impossible) to handle a yarn if the needles are very oversized.
you can, however not go infinitly small with needles, since at some point you will be unable to loop the yarn through your stitch, when the needles are tiny compared to the yarn.
So: between those extremes you can chose your needles in a size that gets you the desired "hole look" or "dense look" or anywhere in between.
The No. 13 may have been an attempt to make the scarf very quick and use very few stitches. (US no. 13 is metric 9mm, right?)
What yarn did you use? How thick is that?