Glove
Softball gloves run an inch longer than baseball gloves. Ages 5-7: 11 inches. Ages 8-10: 11 to 12 inches. Ages 11-12: 12 to 12.5 inches. Ages 13+: 12.5 to 13 inches for fielders, 13 inches for first base.
The web should be deeper than a baseball glove. The ball is bigger.
Same fit test as baseball: kid opens and closes the glove ten times without their hand shaking.
Bat
Same reach and leg tests as baseball.
Drop weight is typically -11 to -12 for fastpitch up to age 12, dropping to -10 for older players. ASA/USA Softball stamp required.
Slowpitch bats are different. If you are not sure, ask the league what stamp they require.
Face mask and helmet
Many fastpitch leagues require a fielder's face mask. Sizing is by youth/adult and adjusts at the chin strap.
Catcher's gear: chest protector (NOCSAE-approved for the kid's age band), shin guards, mask. Sized by height.