Use any cotton yarn you want and a hook that allows you to crochet tight.

Hook & Yarn
I used a hook size 2.5mm and cotton yarn with yardage 170m/50g (185y/1.76oz)

Sizes
The pattern is very scalable. Instructions added.
My small star is around 5cm wide (2”) and the slightly bigger one is 6cm wide (2.4”)

I recommend wash and block for a perfect look. During this you decide if you want bold or sharp star points when you shape your star.