I have used this product to reduce the need for cleaning. It makes cleaning quicker and easier. Accuracy is also less affected by the fouling.
https://shop.dyna-tek.com/product/bore-coat-kit/
For the 12 year old this is what I would use.
https://www.targetsportsusa.com/remington-managed-recoil-300-win-mag-ammo-150-grain-core-lokt-psp-rl300w1-p-1293.aspx
For you I would try several brands to see what shoots well in the rifle. I also would not lock into 200 gr. ammo, any of the mono...
You only need to clean when accuracy goes or at the end of the season before it goes in the safe.
I have found anything north of 2000 fps expands them just fine.
I have used Barnes tsx/ttsx, Nosler e-tips and Hornady gmx and they all work and none seem to be more copper prone than any other...
Graf & sons
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Here is good info on reduced loads. I use trail boss in a 308 for fun loads my granddaughter shoots, she is 10.
https://www.hodgdon.com/resources/data-sheets/
I would go up in the loads. Nosler lists 65 gr. with H4831 and 150's. Lyman goes to 67.5 with nosler 140's. Nosler also lists IMR 4831 [faster than H4831] at 66 gr. with 140's.
For deer hunting I use 150 gr. bullets in my 308. My favorite bullets are Nosler BTs, Sierra Pro Hunters and Hornady ILs. I have taken more deer with the Pro Hunters but am currently using BTs. These all shoot very well in my rifle. You will have to try several to see what works in your...
Bowhunter60
Just know under all those plastic tips is big hollow point. I have taken animals with all you have listed and found them all to work well. Shoot what give you confidence.