[Jasmine Zhou]

This is a really really cool idea. Would these kits be more like little-bags-to-hand-out or baskets-with-things-to-take/borrow?

Everything I'd suggest for such a kit has already been mentioned. For my personal "competition emergency kit", I usually try to have:
hair ties (with extras!), hair clips
feminine supplies (with extras!)
tissues
post or stud earrings (for those annoying-to-reach reset buttons)
a USB flash drive
an extra team shirt
saline solution and a contact lens case (I wear contacts)
writing utensils
and snacks (some with chocolate and some with salt).
The first three are the most reasonable to put into a general kit, but I've needed all of them at at least one competition.