I also really like 165gr game king. I bought some 150gr Barnes XFB (TSX) for a rifle I sold. My others shoot 150gr just fine, so no issue. I also use .308 165gr boat tail for my 7.5x55. Combined Technology are awesome in 7.5x55.
Freedom is not free. The best of us always leave too soon.
I'm guessing since you're 14 years old, you don't handload. Factory ammo in the 150-165 grain range is ideal. You can shoot 180 grain ammo for deer, but why bother.
Different rounds from different companies will give you different shot size groups. If you can afford to go out and shoot different brands to see which kind work best in your rifle, that would be perfect.
If you can't and you're limited to what you can buy, that's alright. Worry less about the bullet weight and worry more about your marksmanship. Nothing is more important than being able to hit your target. If you can't hit it, then it doesn't matter what kind of ammo you shoot.