I don't mean to be rude, but I'm having a hard time following exactly what you want.
Originally you wanted a larger caliber rifle than a .243 for shooting 50-500 yards.
Now you're saying that you'll rarely be shooting the weapon and at ranges of no more than 200 yards on the rare occasion.
Please identify the exact purpose and intended ranges for the rifle and caliber you're looking for suggestions on purchasing.
Otherwise, again, a .308.
Originally you wanted a larger caliber rifle than a .243 for shooting 50-500 yards.
Now you're saying that you'll rarely be shooting the weapon and at ranges of no more than 200 yards on the rare occasion.
Please identify the exact purpose and intended ranges for the rifle and caliber you're looking for suggestions on purchasing.
Otherwise, again, a .308.