Collocations for stool - noun

high, tall
small
three-legged
swivel
step (esp. AmE)
bar, drum, kitchen, milking, piano
an old-fashioned milking stool

wooden

be perched on, perch on, sit (down) on
He was perched on a bar stool, ordering a beer.

get off
pull up
She pulled up a stool next to me.