Needles 9 and 12 mm (not 12,75 mm, I can't choose otherwise here).
S - 600 grams Super Chunky
M - 700 grams Super Chunky
L - 800 grams Super Chunky
XL - 900 grams Super Chunky
A crochet hook, for the loops at the waist
darning needle for the buttons
3 plastic rings of 30 mm for the buttons
By adjusting the needle size you can adjust the sizes of the vest.
If you use needles 10 mm for the bottom ribbing you will get a wider waist, but you will need some more yarn.
If you knit chart XL with needles 10 mm (instead of 9) and 15 mm (instead of 12), you will get a size XXL, but be aware you will need more yarn!