6.5 Creedmor is the perfect kids gun. Super accurate, very little recoil, and every store has a ton of ammo for them.
243 will certainly get the job done within 200 yards. Getting beyond that, good shot placement will be crucial. If you look up the ballistics for a 243, you'll see that at about 300 yards, they're only pushing around 900-1000 pounds of energy. I started out hunting with a 243 and I shot plenty of deer in the 100-250 yard range. I can remember quite a few deer totally crumpling up on the spot from a 100gr Core Lock.