I agree with the idea of a metal water bottle. We all need to stop using plastic, particularly the disposable water bottles that have unregulated water in them and which are transported from city to city using fossil fuels. Not to mention they are subjected to heat during transport and the plastic starts to break down.
Maybe also some reusable sandwich containers that can go in whatever lunch box the parents and child pick out. My stepdaughter's child just went thru kindergarten, and they did a whole unit on recycling. Now my "granddaughter" is all fired up about saving the earth, doesn't want to use baggies that go in the trash, and wants to reduce/reuse. So we got her some sandwich containers and snack boxes, some of which have a gel lid that goes in the fridge - keeps the food cold without her mom having to add one of those separate and somewhat heavy gel packs. There's a company call "Stay Fit" that makes those sandwich containers - you can buy them in the supermarket.
My granddaughter loves these! And they're helping my stepdaughter keep up with environmental issues in a simple way.
A pencil case is a good idea as well - maybe you can find out from the school what materials they will require - our town requires colored pencils as well as regular pencils.
Good luck!