I'm not sure what kind of wool I used (whoops), but you can use whatever kind or weight of wool you like! I think I used 6 or 7mm needles for this though. Can also be knit of circular needles if you find that easier. Experiment with your choosen wool and tension to figure out what you like best!
Stockinette Stitch Pattern
Cast on 42 stitches.
Row 1: knit 14, purl 14, knit 14
Row 2: purl 14, knit 14, purl 14
Repeat Row 1 & 2 for the first 18 rows, or until you've got your desired sized rectangle/sqaure. (this is Stockinette Stitch!)
Row 19 (or whenever you're ready to start creating that checkered look): purl 14, knit 14, purl 14
Row 20: knit 14, purl 14, knit 14
Repeat for another 18 rows, or however many rows you did before.
Keep repeating these squares until you've made your circle scarf as long as you'd like, then join together at the end to form a circle. Make sure you've done an even number of squares so that the pattern is continuous before you join the ends!
My finished scarf measured 10.5 inches wides, by 80 inches in diameter (it wraps around my neck 3 times.)
Disclaimer: I did this a little while ago so I hope this is right, please feel free to correct me if i've made an error or it doesn't make sense :)