Shoes
Court shoes have a flat sole with a herringbone tread. Running shoes do not work and slide on a wood floor.
A high-top is preferred through age 12 because ankle stability matters more than weight at that age. Mid-cut after that.
Buy at the end of the day when feet have swelled. Bring the socks they will play in.
Ball
Size 5 (27.5 inches): ages 5-8.
Size 6 (28.5 inches, intermediate): ages 9-11 boys, ages 9-13+ girls.
Size 7 (29.5 inches, official): boys 12+ and high school.