A .243 would probably be a little too light of a recoil for You...but I love shooting and hunting with my Browning A-bolt Hunter in a .243 with the Hornady 100 grain bullets!I'm thinking a 7mm-o8 would be a very good choice...less recoil and plenty of knock-down power on Whitetails...I'm using a Savage Model 111 GCNS 7mm-08 with the Accu-trigger using 140 grain shells,Millet rings and a Leupold Rifleman matte-black scope in a 3X9X40mm.....not many choices in bullets for the 7mm-o8 but what the heck,the Deer don't complain...You could even go with the Remington "Managed Recoil" shells and it would have even less recoil and a Youth Hunter could hunt with the very same Rifle!

If You reload You could change that bullet weight to say a 120-130 grain and I bet You'd have one fast bullet with good enough punch to slay any good size Doe or Buck!