Questioning iron or optical sights WRT bullet weight makes little sense. Bullet weight - as well as design - should be chosen based on the use the rifle is put to. Sights should be considered after other decisions are made. Don't put the cart before the horse.
You have stated that you wish to shoot out to 300 yards. OK, best accuracy at that distance pretty much eliminates light bullets unless you live where the wind never blows. That means bullets in the 69 ~ 80 grain range would be preferred. That dictates a rate of twist of 1:8 or 1:7. A slower rate is unlikely to provide good accuracy with those weight bullets.
Once a rifle has been acquired with the desired rate of twist, you WILL require a decent scope to test loads for best accuracy. Sure, you can use iron sights but the best load with cutting edge accuracy will be determined using a scope.
You may even consider using two bullets as it's generally accepted that boat-tail bullets don't stabilize until they're past 100 yards. At 100 yards, flat base bullets generally work best. At 200 & 300 yards, a BT bullet should be better. You'll never know until you test your loads and iron sights will NOT provide the best answer.
Now that you have your rifle and load(s), it's time to decide the sight question. Iron sights, especially aperture sights, will be OK on targets large enough for you to see at distance. I've shot .22LR out to 250 yards with irons and done pretty well on reasonably sized targets BUT a properly scoped rifle will be required for targets that can't be seen easily with the naked eye.
So the answer to your curiosity is this: bullet weight selection will be determined by what the rifle likes best. Sights will be determined by just how precise the shooter wants to be but at 200 & 300 yards, a scope is likely to be best.
