First off, since it isn't your rifle, I'd just try the "0" ring. I wouldn't mess with the trigger no matter how bad it is, permission or not. Some guys have good luck with the .243, and others can't get them to shoot. That's why I don't own one. I think the 7mm-08 is more versatile and has a better track record for accuracy, especially if you reload. If you don't reload, with ammo running 20 to 30 bucks plus a box of 20, I'd give it some serious thought. The .223 is a viable option with much less expensive ammo. I know many kids have killed their first deer with a .223, but I believe, to be a deer rifle, it has to be in the hands of a very skilled hunter and marksman who knows where the vitals are from any angle and can put a bullet there. Also, the pistol caliber Handis work well on Whitetails.
Pete