Water bottle:
I think they're a conservative company, but if your kid can handle the weight, Yeti bottles are worth the price. They're dishwasher safe and take a huge beating. There also one of the couple metal bottles I've used that seem to do alright with not making it taste like metal.
Stick with the stock lid. They're a little bit of a pain to drink from since it's a huge hole, but the default lid seems to impart the least amount of plastic and rubber flavor.
If you DON'T want a vacuum insulated bottle, or not even metal, just get a modern 1 liter Nalgene bottle. Those things are also bulletproof. They'll take on more plastic flavor and don't do AS well in the sun, but are cheaper and weigh a lot less. Pair the Nalgene with a decent carabiner around the loop for a useful and fashionable hold and to clip it to stuff like a backpack, lanyard, or desk. I think those 1L Nalgene bottles might also do okay at dishwasher.
Expectation ballpark pricing: the Yetis go for 25-60 USD, Nalgenes go for 10-25.
Don't buy a cup. Those are dumb.
Don't buy a straw, those are dumb.
Hydroflasks are a decent alternative to Yeti and are lighter (and maybe 5-10% cheaper, and maybe less conservative company), but last I saw, are not dishwasher safe. Dishwasher is a big deal to me. Buy a dedicated bottle brush, too. Avoid (used/non brand new) sponges on them because sponges get fucking nasty and you don't want those anywhere near your water supply.
Always ALWAYS ALWAYS smell your water bottle. Smell the inside, smell the opening, smell the lid. Smell = bacterial growth. Having good, clean drinking water is like a fucking art.
Get a water filter, if you can. And treat your hard/soft water if you can.
Good water makes a WORLD of difference, both immediately, and also long term in life. You drink more water, get less bullshit like lead, be more hydrated, it's better for your teeth, your skin, your eyes, your brain, your success, your health, your weight, etc.
If the bottle is too heavy or too cumbersome, the kid won't use it. If the bottle makes the water taste bad at all or isn't fashionable, they won't use it. And if they won't use it, they likely aren't drinking enough water, and maybe drinking other things that are less good for them, instead.