Women's stick (different than a boy's lacrosse stick)/Girls Youth stick for younger players U8. The difference in stick quality is you pay substantially more money for lighter shafts, and more durable plastic heads (crosse). The new player will be just fine in a starter set from STX like the 100, or step up to the 200 or 400. The head shapes are very similar in shape, and a novice player won't notice differences.
Eye protection (ASTM 3077)
Colored Mouthguard (versus clear or white which look like teeth when the referee scans the field for players). A popular mouth guard is the Shock Doctor Gel Max. Form fit to your player's mouth before practice. Consider having a back-up. In the lower age groups, they tend to get lost, because mouth guards are no longer allowed to be attached to the goggles.
Women's Lacrosse Gloves (highly optional)
Cleats (optional, but common, and provide ankle stability on turf. The girls lacrosse cleat is similar to a football cleat, with one toe cleat at the top of the cleat. Popular brands include New Balance, and Under Armour.
